Question

Does the graph show the system of equations x+y=2
𝑥
+
𝑦
=
2
and −x+y=7
−
𝑥
+
𝑦
=
7
? Should the lines for the system be parallel?

(1 point)
Responses

Both graphs are correct. The lines should be parallel.
Both graphs are correct. The lines should be parallel.

The graph of −x+y=7
−
𝑥
+
𝑦
=
7
is incorrect. The lines should be parallel.
The graph of negative x plus y equals 7 is incorrect. The lines should be parallel.

The graph of x+y=2
𝑥
+
𝑦
=
2
is incorrect. The lines should intersect.
The graph of x plus y equals 2 is incorrect. The lines should intersect.

The graph of −x+y=7
−
𝑥
+
𝑦
=
7
is incorrect. The lines should intersect.

Answer 1

Choose: "The graph of −x + y = 7 is incorrect. The lines should intersect."

Reason: x + y = 2 ⇒ y = −x + 2 (slope −1).
−x + y = 7 ⇒ y = x + 7 (slope +1). Slopes are different, so the lines are not parallel; they intersect. (They meet at (-2.5, 4.5).)