Question

Which values of PP and QQ result in an equation with no solutions? -60x+32=Qx+P−60x+32=Qx+P Choose all answers that apply: Choose all answers that apply: (Choice A) A Q=-60Q=−60 and P=60P=60 (Choice B) B Q=32Q=32 and P=60P=60 (Choice C) C Q=-60Q=−60 and P=-32P=−32 (Choice D) D Q=32Q=32 and P=-60P=−60

Answer 1

A and C

Explanation:

Given:

-60x+32 = Qx+P

Find:

Which values of P and Q result in an equation with no solutions? Choose all answers that apply:

(Choice A) A Q=-60 P=60

(Choice B) B Q=32 P=60

(Choice C) C Q=-60 P=−32

(Choice D) D Q=32 P=−60

Solution:

The equation will have no solution if it reduces to ...

0 = (non-zero constant)

If we add 60x-32 to both sides, we get

0 = 60x +Qx + P-32

0 = (Q+60)x +(P-32)

The x-term must be zero, so Q+60 = 0, or Q = -60.

The constant term must be non-zero, so P-32 ≠0, or P ≠ 32.

The appropriate answer choices are those with Q=-60 and P≠32, A and C.