$3x-5y=4$
$9x=2y+7$
Solve the given equations given above using the elimination method and find the value of $x$ and $y$.

The correct option is D $x=\frac{9}{13},y=-\frac{5}{13}$
$3x-5y=4\dots ..\left(1\right)$

$9x=2y+7$
$\Rightarrow 9x-2y=7\dots ..\left(2\right)$

Multiplying equation (1) by 3, we get
$9x-15y=12\dots ..\left(3\right)$

Subtracting equation (2) from equation (3), we get
$-13y=5$
$\Rightarrow y=-\frac{5}{13}$

Substituting the value of $y$ in equation (2), we get
$9x-2(-\frac{5}{13})=7$
$\Rightarrow 9x+\frac{10}{13}=7$
$\Rightarrow 9x=7-\frac{10}{13}$
$\Rightarrow 9x=\frac{91-10}{13}$
$\Rightarrow 9x=\frac{81}{13}$
$\Rightarrow x=\frac{81}{13\times 9}$
$\Rightarrow x=\frac{9}{13}$