Question

If $3x-2y=5$ and $3y-2x=3$ then find the value of $(x+y)$.

Answer 1

$3x-2y=5$............ $\left(1\right)$

$3y-2x=3$

$-2x+3y=3$

Multiply $\left(1\right)$ by $2$ & eq $\left(2\right)$ by $3$

$6x-4y=\mathrm{10..........}\left(3\right)-6x+9y=\mathrm{19..........}\left(4\right)\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_Addingeqn\left(3\right)and\left(4\right),weget$

$6x-4y=10-6x+9y=19\_\_\_\_\_\_\_\_\_\_\_5y=1$

$y=\frac{1}{5}$

Putting the value in

$6x-\frac{4}{5}=10$

$6x=10+\frac{4}{5}=\frac{54}{5}$

$x=\frac{54}{5\times 6}=\frac{9}{5}$

$x=\frac{9}{5}$

Now $x+y=\frac{9}{5}+\frac{1}{5}=\frac{10}{5}$=2$

$x+y=2$