MilenioCinco

Resolver ecuaciones de primer grado

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<span style="font-size: large;">Ecuaciones de primer grado</span></div>
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<span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">Una </span><b style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">ecuación de primer grado</b><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;"> o </span><b style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">ecuación lineal</b><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;"> significa que es un planteamiento de igualdad, involucrando una o más variables a la primera potencia, que no contiene productos entre las variables, es decir, una </span>ecuación<span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;"> que involucra solamente </span><b style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">sumas y restas</b><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;"> de una </span>variable<span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;"> a la </span><b style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">primera potencia</b><span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;">. En todo </span>anillo conmutativo<span style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px;"> pueden definirse ecuaciones de primer grado.</span></div>
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<span class="mw-headline" id="En_una_inc.C3.B3gnita">En una incógnita</span></h2>
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Una ecuación de una variable <img alt="mx + n = 0" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/6/0/6/6060cd23130b3ff967b76785753111ff.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /> definida sobre un cuerpo <img alt="\mathbb{K}" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/f/9/af9d16e96813d92066e49bf89f7b143e.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" />, es decir, con <img alt="\{m,n,x\} \subset \mathbb{K}, m\neq 0" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/8/1/d/81d31a337983ac4509f232f49f4e39a9.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /> donde <i>x</i> es la variable, admite la siguiente solución:</div>
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<img alt="x = - \frac{n}{m}" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/1/a/b/1ab8d1c590d3e45b5edca8416a61402d.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /></div>
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Cuando tanto la incógnita como los coeficientes son elementos de un anillo que no es un cuerpo, el asunto es más complicado ya que sólo existirán soluciones cuando <i>m</i> divide a <i>n</i>:</div>
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<img alt="\exists k: n = m\cdot k \Rightarrow x = -k" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/1/d/a1dc4ab1e14e3b22e2fbe75d77e50ba1.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /></div>
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<span class="mw-headline" id="En_dos_inc.C3.B3gnitas">En dos incógnitas</span></h2>
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En el sistema cartesiano representan rectas. Una forma común de las ecuaciones lineales de dos variables es:</div>
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<img alt=" y = m x + n " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/d/9/7/d97c13890a1fd1d984a5cd1b9df836b8.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" />;</div>
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Donde <img alt="m" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/6/f/8/6f8f57715090da2632453988d9a1501b.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /> representa la pendiente y el valor de <img alt="n" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/7/b/8/7b8b965ad4bca0e41ab51de7b31363a1.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /> determina el punto donde la recta corta al eje Y (la <i>ordenada al origen</i>).</div>
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Algunos ejemplos de ecuaciones lineales:</div>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt=" 3x + 2y = 5 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/e/5/e/e5e9406bb88af8988fe9262c83d97163.png" style="border: none; display: inline; vertical-align: middle;" /></dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt=" 3x + y -5 = -7x + 4y +3 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/1/3/6/13618ebe47bee4ce52f240764ecb20d1.png" style="border: none; display: inline; vertical-align: middle;" /></dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt=" x - y + z = 15 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/2/e/f/2efe329a412c341b04608f3c48604da2.png" style="border: none; display: inline; vertical-align: middle;" /></dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt=" 3x - 2y + z = 20 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/7/7/f/77fb5d85137be6051ecea7d8eecf1c9a.png" style="border: none; display: inline; vertical-align: middle;" /></dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt=" x + 4y - 3z = 10 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/d/9/ad9eb2fdf916f777eb75959a1533e245.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
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<span class="mw-headline" id="Formas_alternativas">Formas alternativas</span></h3>
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Formas complejas como las anteriores pueden reescribirse usando las reglas del álgebra elemental en formas más simples. Las letras mayúsculas representan constantes, mientras <i>x</i> e <i>y</i> son variables.</div>
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<b>Ecuación general</b></div>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="Ax + By + C = 0" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/5/e/a5e71795889fcbb45c6d9c0bf203f34f.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
</dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Aquí <i>A</i> y <i>B</i> no son ambos cero. Representa una línea en el cartesiano. Es posible encontrar los valores donde <i>x</i> e <i>y</i> se anulan.</dd></dl>
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<li style="margin-bottom: 0.1em;"><b>Ecuación segmentaria o simétrica</b></li>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="\frac{x}{E} + \frac{y}{F} = 1" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/5/7/a/57a0100d0c871ac3dec86b23bea1c91f.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
</dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Aquí ni <i>E</i> ni <i>F</i> no pueden ser cero. El gráfico de esta ecuación corta al eje X y al eje Y en <i>E</i> y <i>F</i> respectivamente.</dd></dl>
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<li style="margin-bottom: 0.1em;"><b>Forma paramétrica</b></li>
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<li style="margin-bottom: 0.1em;"><img alt="x = Ut + x_0" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/1/c/a1c143a0072d4c1ffcb395e4cc6bf914.png" style="border: none; display: inline; vertical-align: middle;" /></li>
<li style="margin-bottom: 0.1em;"><img alt="y = Vt + y_0" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/3/6/d/36d417476d0a488517b40f8ab987e744.png" style="border: none; display: inline; vertical-align: middle;" /></li>
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<dl style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.2em; text-align: start;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Dos ecuaciones que deben cumplirse de manera simultanea, cada una en la variable <i>t</i>. Puede convertirse a la forma general despejando <i>t</i> en ambas ecuaciones e igualando. En esta representación puede afirmarse que la recta pasa por el punto <img alt="(x_0, y_0)" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/f/c/6/fc6c713e7eb34f6cb756d754fc2f61db.png" style="border: none; display: inline; vertical-align: middle;" /> y forma con el eje de abcisas un ángulo cuya tangente satisface: <img alt="\tan \alpha = V/U" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/5/3/f/53f1b5b23279e95ab58b8f41a29f0d38.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
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<li style="margin-bottom: 0.1em;"><b>Casos especiales:</b></li>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="y = F" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/3/d/3/3d33aeef7efb365e07674a4b1bca23bf.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
</dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Un caso especial es la forma estándar donde <img alt=" A = 0 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/3/5/7/357e564112c8be448ad371ce602b0658.png" style="border: none; display: inline; vertical-align: middle;" /> y <img alt=" B = 1 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/d/f/8/df8ec499698337941a898ba05461eb34.png" style="border: none; display: inline; vertical-align: middle;" /> . El gráfico es una línea horizontal sin intersección con el eje X o (si <i>F</i> = 0) coincidente con ese eje.</dd></dl>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="x = E" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/c/6/b/c6be0ca027c7c41d3895c8bcab5cad46.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
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<dl style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.2em; text-align: start;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">Otro caso especial de la forma general donde <img alt=" A = 1 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/5/a/a5a2929bc80363d4ffe77ca4cf1911b8.png" style="border: none; display: inline; vertical-align: middle;" /> y <img alt=" B = 0 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/e/e/8/ee829ea61bcc3fb3efccf2a3987528fc.png" style="border: none; display: inline; vertical-align: middle;" />. El gráfico es una línea vertical, interceptando el eje X en <i>E</i>.</dd></dl>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="0 = 0" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/7/b/b/7bb9d941d22396f1ddf635a5cc656c77.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
</dd></dl>
<dl style="background-color: white; color: #252525; font-family: sans-serif; font-size: 14px; line-height: 22.3999996185303px; margin-bottom: 0.5em; margin-top: 0.2em; text-align: start;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;">En este caso, todas las variables fueron canceladas, dejando una ecuación que es verdadera en todos los casos. La forma original (no una tan trivial como la del ejemplo), es llamada identidad. El gráfico es todo el plano cartesiano, ya que lo satisface todo par de números reales <i>x</i> e <i>y</i>.</dd></dl>
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Nótese que si la manipulación algebraica lleva a una ecuación como <b>1 = 0</b> entonces la original es llamada <i>inconsistente</i>, o sea que no se cumple para ningún par de números <i>x</i> e <i>y</i>. Un ejemplo podría ser: <img alt=" 3 x + 2 =3 x - 5 " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/7/e/a7e42d396877d76e3f7ee4bb566d5b69.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" />.</div>
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Adicionalmente podría haber más de dos variables, en ecuaciones simultáneas. Para más información véa: Sistema lineal de ecuaciones.</div>
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<span class="mw-headline" id="Ecuaci.C3.B3n_lineal_en_el_espacio_n-dimensional">Ecuación lineal en el espacio n-dimensional</span></h2>
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Las ecuaciones lineales de varias variables admiten también interpretaciones geométricas, cuando los coeficientes de la ecuación pertenecen a un cuerpo. Así una función lineal de dos variables de la forma</div>
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<img alt=" f(x,y) = a_1 x + a_2 y " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/b/4/1/b410c0e2d27093621305ed2d447f7cd5.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /></div>
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representa un recta en un plano. En varias variables asumiendo que tanto las variables <img alt="x_i \in \mathbb{K}" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/d/0/2/d020c9462eb8f176d280d8d90d7c5cff.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /> y los coeficientes <img alt="x_i \in \mathbb{K}" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/d/0/2/d020c9462eb8f176d280d8d90d7c5cff.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" />, donde <img alt="\mathbb{K}" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/a/f/9/af9d16e96813d92066e49bf89f7b143e.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /> es un cuerpo entonces una ecuación lineal como la siguiente:</div>
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<img alt="f(x_1,x_2,...,x_n) = a_1 x_1 + a_2 x_2 + ... + a_n x_n " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/2/f/b/2fbde6a92589178945e41e063b8e82ae.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /></div>
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representa un hiperplano de <i>n</i>-1 dimensiones en el espacio vectorial n-dimensional <img alt="\mathbb{K}^n" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/4/c/a/4cacaaba641fb31a5f44751b9ca5ba0e.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" />.</div>
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<span class="mw-headline" id="Sistemas_de_ecuaciones_lineales">Sistemas de ecuaciones lineales</span></h3>
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Los sistemas de ecuaciones lineales expresan varias ecuaciones lineales simultáneamente y admiten un tratamiento matricial. Para su resolución debe haber tantas ecuaciones como incógnitas y el determinante de la matriz ha de ser real y no nulo. Geométricamente corresponden a intersecciones de líneas en un único punto (sistema lineal de dos ecuaciones con dos incógnitas), planos en una recta (dos ecuaciones lineales de tres incógnitas) o un único punto (tres ecuaciones lineales de tres incógnitas). Los casos en los que el determinante de la matriz es nulo no poseen solución.</div>
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<img alt="
    \left \{
        \begin{array}{rcrcrcr}
             5 \,x & - & 3 \,y & + & 4 \,z & = & 8 \\
            -3 \,x & + & 2 \,y & + &  6 \,z & = & 5 \\
             4 \,x & - & 5  \,y & + & 3 \,z & = & 3
        \end{array}
    \right .
" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/1/d/6/1d662ff40fac6fa915e9374840dd2964.png" style="border: none; display: inline; margin: 0px; vertical-align: middle;" /></div>
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Si se consideran <i>n</i> ecuaciones de primer grado linealmente independientes defindas sobre un cuerpo entonces existe solución única para el sistema si se dan las condiciones delteorema de Rouché-Frobenius, que puede ser calculada mediante la regla de Cramer que es aplicable a cualquier cuerpo. Si las ecuaciones no son linealmente independientes o no se dan las condiciones del teorema la situación es más complicada. Si el sistema se plantea sobre un anillo conmutativo que no sea un cuerpo, la existencia de soluciones es también más complejas.</div>
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<span class="mw-headline" id="Linealidad">Linealidad</span></h2>
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Una función definida sobre un espacio vectorial es lineal si y solo si se cumple con la siguiente proposición:</div>
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<dl style="margin-bottom: 0.5em; margin-top: 0.2em;"><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="f(x + y) = f(x) + f(y)" class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/c/7/f/c7f612281c07f64b5eaee4b45c4a279d.png" style="border: none; display: inline; vertical-align: middle;" /></dd><dd style="line-height: 1.5em; margin-bottom: 0.1em; margin-left: 1.6em; margin-right: 0px;"><img alt="f(\alpha x) = \alpha f(x) " class="mwe-math-fallback-png-inline tex" src="http://upload.wikimedia.org/math/1/f/9/1f907ddaf24ef5282dc624debd1a0f03.png" style="border: none; display: inline; vertical-align: middle;" /></dd></dl>
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donde <i>α</i> es cualquier escalar. También se llama a <i>f</i> operador lineal</div>
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Ecuaciones de primer grado Una ecuación de primer grado o ecuación lineal significa que es un planteamiento de igualdad, involucrand...

Instalación y activación de Adobe Photoshop CC 2014

2:29 p.m. Unknown 0

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Instalacion de Adobe Photoshop CC 2014 v15.0.0.58 Multilenguaje</h1>
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                  <a href="http://re-direcciona.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" imageanchor="1" style="background-color: white; color: red; font-family: 'trebuchet ms'; font-size: 12px; line-height: 24px; text-align: -webkit-center; text-decoration: none;" target="_blank"><img border="0" src="http://3.bp.blogspot.com/-mtlpJDKlXYU/U6Q_vKeu9LI/AAAAAAABfhc/e6AaCHhlSbk/s500/Adobe.Photoshop.CC.2014.v15.0.0.58.WIN32.Incl.Kg-XFORCE-www.intercambiosvirtuales.org-26.png" style="border: 0px;" /></a></div>
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<span style="font-family: 'trebuchet ms'; font-weight: bold;"></span><span style="font-family: 'trebuchet ms';"><b>Adobe Photoshop CC (2014) v15.0.0.58 Multilenguaje</b><br /><i>Spanish Incl. | Medicina Incl. | 785 MB | 848 MB | 864 MB | 32-BIT & 64-BIT | WIN/MAC |</i></span></div>
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<span style="background-color: white; font-family: 'trebuchet ms'; font-size: 12px; font-weight: bold; line-height: 24px; text-transform: uppercase;"><u><span style="color: #351c75;">DESCRIPCIÓN</span></u></span></div>
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<span style="background-color: white; font-family: 'trebuchet ms'; font-size: 12px; line-height: 24px; text-align: justify;">Mayor libertad, velocidad y potencia para hacer realidad imágenes increíbles. Conseguirás decenas de funciones nuevas y renovadas, entre las que se incluye la herramienta de enfoque más avanzada del mercado. Comparte tu trabajo directamente desde Photoshop® CC en Behance® para recibir comentarios y mostrar tus propios proyectos. Accede a funciones nuevas en cuanto estén disponibles. Disfruta de todo tu mundo creativo en un único lugar.</span></div>
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<b>Descubre las principales funciones nuevas</b><br />Photoshop CC incluye muchas novedades. Utiliza la herramienta Enfoque suavizado completamente nueva para destacar los detalles. Convierte instantáneas con baja resolución en grandes imágenes con alta resolución. Consigue las avanzadas herramientas de análisis de imagen y edición en 3D que antes solo se ofrecían en Adobe® Photoshop Extended. Todo ello y mucho más.</div>
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<b>Enfoque suavizado completamente nuevo</b><br />Consigue imágenes nítidas y claras en todo momento. Ahora, Enfoque suavizado resalta los detalles y la textura, elimina los efectos de halo y el ruido, y te permite realizar ajustes para conseguir el aspecto concreto que deseas. Es todo lo que necesitas para lograr la nitidez.</div>
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<b>Integrado en Creative Cloud</b><br />Con Photoshop CC, integrado en Creative Cloud, tu proceso creativo será fluido e intuitivo y contará con una mayor conectividad. Consíguelo como un abono a una aplicación única o con un abono completo a Creative Cloud, que también incluye el resto de las herramientas creativas.</div>
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<u><b><span style="color: #351c75;">Requisitos.</span></b></u></div>
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<span style="background-color: white; font-family: 'trebuchet ms'; font-size: 12px; line-height: 24px; text-align: justify;"><b>Windows</b></span><span style="background-color: white; font-family: 'trebuchet ms', Verdana, Arial, Helvetica, sans-serif; font-size: 12px; line-height: 24px; text-align: justify;"></span><ul style="background-color: white; font-family: 'trebuchet ms', Verdana, Arial, Helvetica, sans-serif; font-size: 12px; line-height: 24px; text-align: justify;">
<li><span style="font-family: 'trebuchet ms';">Procesador Intel® Pentium® 4 o AMD Athlon® de 64 bits. (de 2 GHz o superior).</span></li>
<li><span style="font-family: 'trebuchet ms';">Microsoft® Windows® 7 con Service Pack 1 o Windows 8.</span></li>
<li><span style="font-family: 'trebuchet ms';">1 GB de RAM.</span></li>
<li><span style="font-family: 'trebuchet ms';">2,5 GB de espacio disponible en el disco duro para la instalación; se requiere espacio libre adicional durante la instalación (no se puede instalar en dispositivos de almacenamiento flash extraíbles).</span></li>
<li><span style="font-family: 'trebuchet ms';">Resolución de 1024 x 768 (se recomienda 1280 x 800) con tarjeta gráfica OpenGL® 2.0, color de 16 bits y 512 MB de VRAM (se recomienda 1 GB)*</span></li>
<li><span style="font-family: 'trebuchet ms';">Se requiere disponer de una conexión a Internet y registrarse para la activación del software y la validación de los abonos obligatorias, y para el acceso a los servicios online†.</span></li>
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<span style="font-family: 'trebuchet ms';"><b>Mac OS</b></span></div>
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<li><span style="font-family: 'trebuchet ms';">Procesador Intel multinúcleo con compatibilidad de 64 bits.</span></li>
<li><span style="font-family: 'trebuchet ms';">Mac OS X v10.7 o v10.8.</span></li>
<li><span style="font-family: 'trebuchet ms';">1 GB de RAM.</span></li>
<li><span style="font-family: 'trebuchet ms';">3,2 GB de espacio disponible en el disco duro para la instalación; se requiere espacio libre adicional durante la instalación (no se puede instalar en un volumen que utilice un sistema de distinción entre mayúsculas y minúsculas en archivos, ni en dispositivos de almacenamiento flash extraíbles).</span></li>
<li><span style="font-family: 'trebuchet ms';">Resolución de 1024 x 768 (se recomienda 1280 x 800) con tarjeta gráfica OpenGL 2.0, color de 16 bits y 512 MB de VRAM (se recomienda 1 GB)*.</span></li>
<li><span style="font-family: 'trebuchet ms';">Se requiere disponer de una conexión a Internet y registrarse para la activación del software y la validación de los abonos obligatorias, y para el acceso a los servicios online†.</span></li>
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<span style="font-family: 'trebuchet ms';">* Las funciones 3D estarán desactivadas si hay menos de 512 MB de VRAM.</span></div>
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<u><b><span style="color: #351c75;">Manual de instalacion y activacion. </span></b></u></div>
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<a href="http://re-direcciona.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" imageanchor="1" style="background-color: white; color: red; font-family: 'trebuchet ms'; font-size: 12px; line-height: 24px; text-align: -webkit-center; text-decoration: none;" target="_blank"><img border="0" src="http://4.bp.blogspot.com/-Vit3u_vUukI/U6Q_mhbecwI/AAAAAAABffQ/90SpjdREHPE/s500/Adobe.Photoshop.CC.2014.v15.0.0.58.WIN32.Incl.Kg-XFORCE-www.intercambiosvirtuales.org-01.png" style="border: 0px;" /></a><span style="background-color: white; 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Instalación y activación de Adobe Photoshop CC 2014

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