Question

Solve the following simultaneous equations:
$12x+13y=62$;
$13x+12y=63$

Answer 1

The given simultaneous equations are,

$12x+13y=62$ ... (1)

$13x+12y=63$ .... (2)

Multiply equation (1) by $12$ and equation (2) by $13$,

$(12x+13y)\times 12=62\times 12$

$(13x+12y)\times 13=63\times 13$

On simplifying, we get,

$144x+156y=744$ .... (3)

$169x+156y=819$ .... (4)

Subtracting equation (3) from (4), we get

$25x=75$

$\Rightarrow x=\frac{75}{25}=3$

Substituting the value of $x$ in equation $\left(1\right)$, we get

$12\left(3\right)+13y=62$

$\Rightarrow 36+13y=62$

$\Rightarrow 13y=62-36$

$\Rightarrow y=26$

$\Rightarrow y=\frac{26}{13}$

$\Rightarrow y=2$