How do you solve the system $-3(5+x)=y$ and $5(x-3)=2y+4$ ?

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Answer 1 · 2015-06-09T14:36:06

The solution for the system of equations is:
$color(blue)( x = -1 , y =-12$

$-3(5+x)=y$
$-15 -3x = y$
$y +3x = -15$ ............equation $(1)$

$5x-15=2y+4$
$5x - 2y = 4 +15$
$5x - color(blue)(2y) = 19$ ................equation $(2)$

Multiplying equation $(1)$ by $2$
$y +3x = -15$
$color(blue)( 2y)+6x = -30$ ...........equation $(3)$
Adding equations $2 and 3$ to eliminate $color(blue)(2y)$

$5x - cancelcolor(blue)(2y) = 19$
$cancelcolor(blue)( 2y)+6x = -30$
$11x = -11$
$color(blue)(x = -1$

Substituting $x$ in equation $(1)$ to find $y$ :
$y = -15-3x$
$y = -15-3.(-1)$
$color(blue)(y = -12$

How do you solve the system -3(5+x)=y-3(5+x)=y and 5(x-3)=2y+45(x-3)=2y+4?