Question

For which values of P and Q does the following equation have infinitely many solutions ?

Px+57=-75x+Q

Answer 1

(P, Q) = (-75, 57)

Explanation:

The equation will have infinitely many solutions when it is a tautology.

Subtract the right side from the equation:

Px +57 -(-75x +Q) = 0

x(P+75) +(57 -Q) = 0

This will be a tautology (0=0) when ...

P+75 = 0

P = -75

and

57-Q = 0

57 = Q

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These values in the original equation make it ...

-75x +57 = -75x +57 . . . . . a tautology, always true