Question

5x+ 3y= 21 7x + 8y = 37 sustitucion​

Answer 1

             METODO DE SUSTITUCION

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Operamos

$\begin{bmatrix}5x+3y=21\\ 7x+8y=37\end{bmatrix}$

Resolvemos 1ra ecuación para "x"

$5x+3y=21$

$5x+3y-3y=21-3y$

$5x=21-3y$

$\frac{5x}{5}=\frac{21}{5}-\frac{3y}{5}$

$x=\frac{21-3y}{5}$

Sustituimos "x" en la 2da ecuación

$\mathrm{Sustituir\:}x=\frac{21-3y}{5}$

$\begin{bmatrix}7\cdot \frac{21-3y}{5}+8y=37\end{bmatrix}$

$=\frac{-21y+147}{5}+8y$

$=\frac{147-21y}{5}+\frac{8y\cdot \:5}{5}$

$=\frac{147-21y+8y\cdot \:5}{5}$

$147-21y+8y\cdot \:5$

$=147-21y+40y$

$=147+19y$

$=\frac{147+19y}{5}$

$=\frac{147}{5}+\frac{19y}{5}$

$\frac{147}{5}+\frac{19y}{5}=37$

$\frac{147}{5}\cdot \:5+\frac{19y}{5}\cdot \:5=37\cdot \:5$

$\frac{147}{5}\cdot \:5=147$

$\frac{19y}{5}\cdot \:5=19y$

$37\cdot \:5=185$

$147+19y=185$

$147+19y-147=185-147$

$19y=38$

$y=\frac{38}{19}$

$y=2$

Despejamos para "x"

$\mathrm{Para\:}x=\frac{21-3y}{5}$

$\mathrm{Sustituir\:}y=2$

$x=\frac{21-3\cdot \:2}{5}$

$x=\frac{15}{5}$

$x=3$

$\mathrm{Las\:soluciones\:para\:el\:sistema\:de\:ecuaciones\:son}$

$x=3,\:y=2$

RPTA :  x = 3     y = 2