Question

Find the values of P and Q for which the following systems of equations has infinite no. of solutions
2x+3y=7;(p+q)x+(2p-q)y=21

Answer 1

$\frac{a1}{a2} = \frac{b1}{b2} = \frac{c1}{c2} \\ \frac{2}{p + q} = \frac{3}{2p - q} = \frac{7}{21} = \frac{1}{3} \\ p + q = 6\\ 2p - q = 9 \\ add \: both \: eq \\ 3p = 15 \\ p = 5 \: \: \: \: ans \\ 5 + q = 6 \\ q = 1 \: \: \: ans$