Question

If pb = aq, qc = br and pc = ar, then the system of equations px + qy = r and ax + by = c (a, b, c, p, q, r ≠ 0)

• A. Has a unique solution
• B. Has no solution
• C. Has infinitely many solutions
• D. Has exactly two solutions

Answer 1

The correct option is C Has infinitely many solutions

Given : pb = aq. qc = br and pc = ar
$\Rightarrow \frac{p}{a}=\frac{q}{b},\frac{q}{b}=\frac{r}{c}and\frac{p}{a}=\frac{r}{c}$
$\Rightarrow \frac{p}{a}=\frac{q}{b}=\frac{r}{c}......\left(i\right)$

Consider the system of equations $px+qy=r$ and ax + by = c.
Then from (i), $\frac{p}{a}=\frac{q}{b}=\frac{r}{c}.$
Therefore, the system of equations has infinitely many solutions.
Hence, the correct answer is option (3).