Question

vA linear equation is graphed on the coordinate grid below.





image.png





When graphed on the same coordinate grid, which equation results in a system of equations with exactly one solution?




3
x
+
2
y
=
−
2


x
+
2
y
=
2


6
x
+
4
y
=
8


6
x
+
4
y
=
−
12

Answer 1

x + 2y = 2

Reason: The graphed line has slope −3/2. Equations 3x+2y=−2, 6x+4y=8, and 6x+4y=−12 all have slope −3/2 (so they are parallel to the graphed line), so they would give no solution or be the same line. x+2y=2 has slope −1/2, different from −3/2, so it will intersect the graphed line exactly once.