Question

Solve : $9x-4y=8$ and $13x+7y=101$.

• A. $x=4,y=7$
• B. $x=0,y=4$
• C. $x=6,y=14$
• D. $x=7,y=13$

Answer 1

The correct option is A $x=4,y=7$

Given equations are

$9x-4y=8$ ....(1)

and $13x+7y=101$ ....(2)

Solving equation (1), we get

$9x=8+4y\Rightarrow x=\frac{8+4y}{9}$ ....(3)

Put this value in equation (2), we get

$13\left(\frac{8+4y}{9}\right)+7y=101$

$\Rightarrow 104+52y+63y=909$

$\Rightarrow 115y+104=909$

$\Rightarrow 115y=805$

$\Rightarrow y=7$

Substitute this value of $y$ in equation (3), we get

$x=\frac{8+4\left(7\right)}{9}$

$\Rightarrow \frac{36}{9}$

$\Rightarrow x=4$

Therefore, the solution is $x=4,y=7$.