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

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Answer 1 · 2017-08-04T03:22:16

(2,-2)

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

Solve the second equation for x:

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

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

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

Solve for y:

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

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

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

$(2, - 2)$ $(2,-2)$

Check:

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

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

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