Question

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

A.
−
2
x
+
6
y
=
−
12

B.
3
x
−
9
y
=
9

C.
x
−
3
y
=
6

D.
9
x
−
3
y
=
6

Answer 1

First put each equation into slope-intercept form y = mx + b.

A: −2x + 6y = −12 → y = (1/3)x − 2
B: 3x − 9y = 9 → y = (1/3)x − 1
C: x − 3y = 6 → y = (1/3)x − 2
D: 9x − 3y = 6 → y = 3x − 2

A and C are the same line (same slope and intercept). B is parallel to A/C (same slope, different intercept) so gives no intersection. D has a different slope (3 vs 1/3), so it will intersect any of the others in exactly one point.

Answer: D.