Answer
$(3,0)$
Work Step by Step
To solve this system of equations, we use the graphing method.
$2x+y=6$
$2x-y=6$
Taking the first equation, we solve for y.
$2x+y=6$
$y=6-2x$
Find three solutions:
For x=2,
$y=6-2(2)$
$y=6-4$
$y=2$
For x=0,
$y=6-2(0)$
$y=6-0$
$y=6$
For x=-2,
$y=6-2(-2)$
$y=6+4$
$y=10$
With the three points, $(2,2), (0,6), (-2,10)$, we can graph the straight line that goes through these points.
Taking the second equation, we solve for y.
$2x-y=6$
$-y=6-2x$
$y=2x-6$
Find three solutions:
For x=2,
$y=2(2)-6$
$y=4-6$
$y=-2$
For x=0,
$y=2(0)-6$
$y=0-6$
$y=-6$
For x=-2,
$y=2(-2)-6$
$y=-4-6$
$y=-10$
With the three points, $(2,-2), (0,-6), (-2,-10)$, we can graph the straight line that goes through these points.
The intersection point between these two lines is the answer to the system of equations.
