Question

Solve the following system of equations:

$\frac{x}{7}+\frac{y}{3}=5$

$\frac{x}{2}-\frac{y}{9}=6$

Answer 1

Given system of equations:
$\frac{x}{7}+\frac{y}{3}=5$ and $\frac{x}{2}-\frac{y}{9}=6$
$\Rightarrow \frac{3x+7y}{21}=5$ and $\Rightarrow \frac{9x-2y}{18}=6$
$\Rightarrow 3x+7y=105$ .........(i)and
$9x-2y=108$ .........(ii)
From $3\times \text{eq}\left(i\right)-\text{eq(ii)}$
$\Rightarrow 9x+21y-9x+2y=315-108$
$\Rightarrow 23y=207$
$\Rightarrow y=\frac{207}{23}$
$\therefore y=9$
Substitute $y=9$ in equation(i), we get
$3x+7\left(9\right)=105\Rightarrow 3x+63=105\Rightarrow 3x=105-63$
$\Rightarrow 3x=42$
$\Rightarrow x=\frac{42}{3}$
$\Rightarrow x=14$
Hence, the value of $x$ and $y$ is $x=14,y=9$.