Question

Match each system on the left with all words that describe the system on the right. Choices on the right can be used more than once.
y=3x-1
2y-6x=4

2y=-x+6
4y+2x=12

y=2x+3
x+y=-9

inconsistent
consistent
independent
dependent

Answer 1

1) y = 3x − 1 and 2y − 6x = 4 — inconsistent
Reason: substituting y gives 2(3x−1)−6x = 4 → −2 = 4 (contradiction), so no solution.

2) 2y = −x + 6 and 4y + 2x = 12 — consistent, dependent
Reason: first rearranges to x + 2y = 6; second is 2(x + 2y) = 12, same line → infinitely many solutions.

3) y = 2x + 3 and x + y = −9 — consistent, independent
Reason: substitution gives 3x + 3 = −9 → x = −4, y = −5, a single unique solution.