Question

Solve for x and y:

$99x+101y=499$;

$101x+99y=501$

Answer 1

Given equation are

$99x+101y=499---\left(1\right)$

$101x+99y=501---\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$

$200x+200y=1000$

$\therefore x+y=5---\left(3\right)$

Subtracting $\left(1\right)$ from $\left(2\right)$

$2x-2y=2$

$\therefore x-y=1---\left(4\right)$

Adding $\left(3\right)$ and $\left(4\right)$

$2x=6\therefore x=3$

Putting $x=3$ in equation $\left(4\right)$

$3-y=1\therefore y=2$

$\therefore y=2,x=3$