Question

Which of the following statements is true of the system below?
–2x – 3y = –1
3x + 6y = 0

The solution to this system is (3, –2).

The solution to this system is (2, –1).

This system has no solutions.

This system has infinitely many solutions.

Answer 1

The true statement is: "The solution to this system is (2, −1)."

Check: For (2, −1),
- First equation: −2(2) − 3(−1) = −4 + 3 = −1 ✓
- Second equation: 3(2) + 6(−1) = 6 − 6 = 0 ✓

The two equations are not scalar multiples, so the solution is unique.