Question

A system of equations has 1 solution. If 4x – y = 5 is one of the equations, which could be the other equation?

y = –4x + 5
y = 4x – 5
2y = 8x – 10
–2y = –8x – 10

Answer 1

4x − y = 5 ⇒ y = 4x − 5 so the slope is 4. For exactly one solution the other line must have a different slope.

Check options:
- y = −4x + 5 has slope −4 (different) → one intersection ✅
- y = 4x − 5 is the same line → infinitely many solutions
- 2y = 8x − 10 ⇒ y = 4x − 5 is the same line → infinitely many
- −2y = −8x − 10 ⇒ y = 4x + 5 has same slope 4 but different intercept → no solutions

So the correct choice is y = −4x + 5.