Question

Which ordered pairs in the form (x, y) are solutions to the equation

4x−5y=24

Select each correct answer.

Responses

(4, 8)
Begin ordered pair 4 comma 8 end ordered pair

(6, 0)
Begin ordered pair 6 comma 0 end ordered pair

(1, −4)
Begin ordered pair 1 comma negative 4 end ordered pair

(−9, −12)

Answer 1

To find which ordered pairs are solutions to the equation \( 4x - 5y = 24 \), we can substitute each pair into the equation and see if it holds true.

1. **For (4, 8)**:
\[
4(4) - 5(8) = 16 - 40 = -24 \quad (\text{not a solution})
\]

2. **For (6, 0)**:
\[
4(6) - 5(0) = 24 - 0 = 24 \quad (\text{is a solution})
\]

3. **For (1, -4)**:
\[
4(1) - 5(-4) = 4 + 20 = 24 \quad (\text{is a solution})
\]

4. **For (−9, −12)**:
\[
4(-9) - 5(-12) = -36 + 60 = 24 \quad (\text{is a solution})
\]

The ordered pairs that are solutions to the equation \( 4x - 5y = 24 \) are:
- \( (6, 0) \)
- \( (1, -4) \)
- \( (-9, -12) \)

Thus, the correct answers are:
- (6, 0)
- (1, -4)
- (−9, −12)