Question

What is the solution of the pair of linear equations $3x–5y=4$, $9x=2y+7$?

• A. $x=\frac{9}{13}$, $y=\frac{-5}{13}$
• B. $x=\frac{13}{9}$, $y=\frac{-13}{5}$
• C. $x=\frac{-9}{13}$, $y=\frac{-5}{13}$
• D. $x=\frac{9}{13}$, $y=\frac{5}{13}$

Answer 1

The correct option is A $x=\frac{9}{13}$, $y=\frac{-5}{13}$

$3x–5y=4$......(1)

$9x=2y+7$
$9x-2y=7$.....(2)

On multiplying equation (1) by 3, we get

$9x–15y=12$.......(3)

On subtracting (2) from (3), we get

$-13y=5$

$\Rightarrow y=\frac{-5}{13}$

On substituting the value of $y$ in (2), we get

$9x=2y+7$

$\Rightarrow x=\frac{7+2y}{9}$

$\Rightarrow x=\frac{7-\frac{10}{13}}{9}$ = $\frac{81}{13\times 9}$

$\Rightarrow x=\frac{9}{13}$