Question

Solve the following equations by substitution method.

$\frac{1}{x}+\frac{2}{y}=9;\frac{2}{x}+\frac{1}{y}=12(x\ne 0,y\ne 0)$

• A. $x=\frac{1}{5},y=\frac{1}{2}$
• B. $x=\frac{2}{5},y=\frac{1}{2}$
• C. $x=\frac{1}{5},y=\frac{-1}{2}$
• D. None of these

Answer 1

Answer: (A)

$x=\frac{1}{5},y=\frac{1}{2}$

Given equations,

$\frac{1}{x}+\frac{2}{y}=9$..............(1)

$\frac{2}{x}+\frac{1}{y}=12$..............(2)

$\frac{1}{x}=9-\frac{2}{y}$.........from (1)

putting value of $\frac{1}{x}$ in (2), we get

$2[9-\frac{2}{y}]+\frac{1}{y}=12$

$18-\frac{3}{y}=12$

$6=\frac{3}{y}$......$y=\frac{1}{2}$

putting value of $y$ in (1), we get

$\frac{1}{x}=9-4$

$\frac{1}{x}=5$......$x=\frac{1}{5}$