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How do you solve x+3y=-2, 2x-y=10?

1 Answer

Sep 8, 2015

The solutions for the system of equations is
$x = 4, y = - 2$ $color(blue)(x=4, y=-2$

Explanation:

$x + 3 y = - 2$ $x+3y=-2$ , multiplying this equation by $2$ $2$
$2 x + 6 y = - 4$ $color(blue)(2x)+6y=-4$ ......equation $1$ $1$

$2 x - y = 10$ $color(blue)(2x)-y=10$ .....equation $2$ $2$

Solving by elimination.

Subtracting equation $2$ $2$ from $1$ $1$ results in elimination of $2 x$ $color(blue)(2x$

$cancelcolor(blue)(2x)+6y=-4$
$-cancelcolor(blue)(2x)+y=-10$
$7y =-14$
$color(blue)(y=-2$

Finding $x$ by substituting $y$ in equation $1$
$x+3y=-2$
$x+3*(-2)=-2$
$x-6=-2$
$x=-2+6$
$color(blue)(x=4$

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