What ordered pair (x,y) satisfies the system of equations $2x-y=6$ and $x+2y = -2$ ?

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Answer 1 · 2017-08-04T03:22:16

(2,-2)

$2x - y =6$
$x+2y=-2$

Solve the second equation for x:

$x+2y=-2$
$x=-2-2y$

Replace x with -2-2y in the first equation:

$2(-2-2y)-y=6$
$-4-4y-y=6$

Solve for y:

$-4-5y=6$
$-5y=10$
$y=-2$

Replace y with -2 in the second equation and solve for x:

$x+2(-2)=-2$
$x-4=-2$
$x=2$

$(2,-2)$

Check:

$2(2)-(-2)=6$
$6=6$

$2+2(-2)=-2$
$-2=-2$

What ordered pair (x,y) satisfies the system of equations 2x-y=62x-y=6 and x+2y = -2x+2y = -2?