Question

Which values of P and Q result in an equation with no solutions?

Px-45=Qx+75

Choose all answers that apply:


A: P = -45 and Q = -75
B: P = 15 and Q = 75
C: P = 45 and Q = -15
D: P = 15 and Q = 15

Also, could you please leave the steps on how to solve this?
-Thanks

Answer 1

Try this solution/explanation:

way 1:

rule: for an equation where no roots P+Q=0. It means, Px-Qx=0, ⇔ x(P-Q)=0, ⇔ P=Q.

for answer 'D' P=Q=15.

way 2:

rule: if an equation of the line has a form y=kx+b, then y₁||y₂ if k₁=k₂. It means, for y₁=Px-45 || y₂=Qx+75, then P=Q. P=Q, if 'D' answer.

Answer: D