Question

Solve for $x$ and $y$, if $2x+3y=8$ and $x+2y=5$.

• A. $x=1,y=2$
• B. $x=-1,y=-2$
• C. $x=-2,y=2$
• D. $x=-1,y=2$

Answer 1

The correct option is A $x=1,y=2$

$2x+3y=8$ .............(1)
and $x+2y=5$ .......(2)
From (1), we get $x=\frac{8-3y}{2}$ .......... (3)
From (2), we get $x=5-2y$ .......... (4)
$\therefore \frac{8x-3y}{2}=5-2y$
or $8x-3y=10-4y$ or $3y=10-4y$ or $y=2$
Using $y=2$ in (4), we get $x=5-4=1$. Therefore,
$x=1,y=2$