Question

Solve the following system of equations by the method of substitution:
$3x-7y=7$, $11x+5y=87$

Answer 1

Given equations are

$3x-7y=7$ ....(1)

and $11x+5y=87$ ....(2)

Therefore, $3x=7+7y\Rightarrow x=\frac{7+7y}{3}$ ....(3)

Put this value of $x$ in equation (2)

$11\left(\frac{7+7y}{3}\right)+5y=87$

$\Rightarrow 77+77y+15y=261$

$\Rightarrow 92y=261-77$

$\Rightarrow 92y=184$

$\Rightarrow y=2$

Put this value in equation (3)

Therefore, $x=\frac{7+7\left(2\right)}{3}$

$\Rightarrow x=\frac{21}{3}$

$\Rightarrow x=7$

Therefore, solution is $x=3,y=2$.