Question

A system of equations is shown below.

{
x
−
y
=
2
x
+
y
=
−
2
Which graph represents this system of equations and its solution?

A.
The graph shows a line labeled x plus y equal to -2 passes through (0, -2) and (2, 0). Another line labeled x minus y equal to 2 passes through (0, 0) and (2, 2).

B.
The graph shows two lines intersecting at (0, -2). A line labeled x plus y equal to -2 passes through (0, -2) and (2, 0). Another line labeled x minus y equal to 2 passes through (0, -2) and (2, 4).

C.
The graph shows two lines intersecting at (2, 0). A line labeled x plus y equal to -2 passes through (0, 2) and (2, 0). Another line labeled x minus y equal to 2 passes through (0, -2) and (2, 0).

D.
The graph shows two lines intersecting at (0, -2). A line labeled x plus y equal to -2 passes through (-2, 0) and (0, -2). Another line labeled x minus y equal to 2 passes through (0, -2) and (2, 0).

Answer 1

Solve: x - y = 2 and x + y = -2. Add: 2x = 0 → x = 0. Then y = -2. So the lines intersect at (0, -2).

Check option D: x + y = -2 passes through (-2,0) and (0,-2); x - y = 2 passes through (0,-2) and (2,0). Both are correct, so answer D.