Question

Solve:

$217x+131y=913$ and
$131x+217y=827$.

Answer 1

We have,
$217x+131y=913$ (i)
$131x+217y=827$ (ii)

Adding equations (i) and (ii), we get
$348x+348y=1740\Rightarrow x+y=5$ (iii)

Subtracting equation (ii) from equation (ii), we get
$86x-86y=86\Rightarrow x-y=1$ (iv)

Adding equation (iii) and (iv), we get
$2x=6\Rightarrow x=3$

Putting $x=3$ in equation(iii), we get $y=2$

Hence, $x=3$ and $y=2$ is the solution of the given system of equations.