Question

d) 1/x + 3/y = 7
4/x - 2/y = 1

Answer 1

Given,

$\frac{1}{x}+\frac{3}{y}=7$

$\frac{4}{x}-\frac{2}{y}=1$

Let, assume $\frac{1}{x}=a$ and $\frac{1}{y}=b$

$a+3b=7$___(1)

$4a-2b=1$____(2)

Multiply by  $4$ with equation (1)

$4a+12b=28$____(3)

Subtract equation (2) from equation (3)

$4a+12b-4a+2b=28-1$

$14b=27$

$b=\frac{27}{14}$

Substitute $b= \frac{27}{14}$ in equation (2)

$4a-2\times\frac{27}{14}=1$

$4a=1-\frac{7}{27}$

$4a=\frac{20}{27}$

$a= \frac{5}{27}$

We know that,

$a= \frac{1}{x}= \frac{5}{27}$

$b=\frac{1}{y}= \frac{27}{14}$

Therefore, the values of $\frac{1}{x}$ and $\frac{1}{y}$ are $\frac{5}{27}$ and $\frac{27}{14}$.