If $p x+2 y=7$ and $3 x+q y=5$ represent the same straight line, then $p$ equals
(A) 5
(B) 7
(C) 21
(D) $\frac{21}{5}$
(E) $\frac{10}{7}$
If $p x+2 y=7$ and $3 x+q y=5$ represent the same straight line, then $p$ equals
(A) 5
(B) 7
(C) 21
(D) $\frac{21}{5}$
(E) $\frac{10}{7}$

## Solution

If we multiply the equation of the first line by 5 and the second by 7 we obtain, $5 p x+10 y=35$ and $21 x+7 q y=35$. Comparing coefficients gives, $5 p=21$ or $p=\frac{21}{5}$.