Question

Find the values of p and q for which the following system of equations has infinite number of solutions :

$2x+3y=7$

$(p+q)x+(2p-q)y=21$

Answer 1

The given system of equations has infinite number of solutions :

$\frac{2}{p+q}=\frac{3}{2p-q}=\frac{7}{21}$

$\frac{2}{p+q}=\frac{3}{2p-q}=\frac{1}{3}$

$\frac{2}{p+q}=\frac{1}{3}$ and $\frac{3}{2p-q}=\frac{1}{3}$

$p+q=6$ and $2p-q=9$

$(p+q)+(2p-q)=15$

$3p=15$

$p=5$

$q=1$