Question

Solve by elimination method: $13x+11y=70,11x+13y=74$.

Answer 1

$13x+11y=70---eqn\left(1\right)$

$11x+13y=74---eqn\left(2\right)$

Multiplying $eqn\left(1\right)$ with $11$

$11(13x+11y)=11\times 70$

$⟹143x+121y=770---eqn\left(3\right)$

Multiplying $eqn\left(2\right)$ with $13$

$13(11x+13y)=13\times 74$

$143x+169y=962---eqn\left(4\right)$

Subtracting $eqn\left(3\right)$ from $eqn\left(4\right)$ we get,

$48y=192$ $⟹y=4$

Now let us eliminate y.

Multiplying $eqn\left(1\right)$ with 13 then we get,

$169x+143y=910---eqn\left(5\right)$

Multiplying $eqn\left(2\right)$ with 11, we get

$121x+143y=814----eqn\left(6\right)$

Subtracting $eqn\left(6\right)$ from $eqn\left(5\right)$,we get $x=2$

So $x=2$ and $y=4$ is our solution