Solve the following equation and verify your answer: 1-9y 19-3y =… - Vidyadip

Question

Solve the following equation and verify your answer:
$\frac{1-9\text{y}}{19-3\text{y}}=\frac{5}{8}$

✓

Answer

$\frac{1-9\text{y}}{19-3\text{y}}=\frac{5}{8}$By cross multiplication:
$5(19-3\text{y})=8(1-9\text{y})$ $\Rightarrow95-15\text{y}=8-72\text{y}$ $\Rightarrow15\text{y}+72\text{y}=8-95$ $\Rightarrow57\text{y}=-87$ $\Rightarrow\text{y}=\frac{-87}{57}=\frac{-29}{19}$ $\therefore\text{y}=\frac{-29}{19}$Verification:
$\text{L.H.S.}=\frac{1-9\text{y}}{19-3\text{y}}=\frac{1-9\Big(\frac{-29}{19}\Big)}{19-3\Big(\frac{-29}{19}\Big)}=\frac{1+\frac{261}{19}}{91+\frac{87}{19}}$ $=\frac{\frac{19+261}{19}}{\frac{361+87}{19}}=\frac{\frac{280}{19}}{\frac{448}{19}}\times\frac{19}{448}$ $=\frac{280}{448}=\frac{280\div56}{448\div56}=\frac{5}{8}=\text{R.H.S.}$

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