Question

Solve the following equations and verify your answer :

$\frac{2-y}{y+7}=\frac{3}{5}$

Answer 1

$\frac{2-y}{y+7}=\frac{3}{5}$

By cross multiplication :

$3(y+7)=5(2-y)$

$\Rightarrow 3y+21=10-5y$

$\Rightarrow 3y+5y=10-21$ (By transposition)

$\Rightarrow 8y=-11\Rightarrow y=\frac{-11}{8}$

$\therefore y=\frac{-11}{8}$

Verification :

$L.H.S.=\frac{2-y}{y+7}=\frac{2+\frac{11}{8}}{\frac{-11}{8}+7}$

$=\frac{\frac{16+11}{8}}{\frac{-11+56}{8}}=\frac{\frac{27}{8}}{\frac{45}{8}}=\frac{27}{8}\times \frac{8}{45}=\frac{27}{45}=\frac{3}{5}=R.H.S.$