Question

Solve following pair of equations by equating the coefficient method:

$x+2y=11$
$2x-y=2$

• A. $x=3,y=4$
• B. $x=5,y=4$
• C. $x=-1,y=-1$
• D. $x=6,y=-4$

Answer 1

The correct option is A $x=3,y=4$

Multiply the equation $x+2y=11$ by $2$ to make the coefficients of $x$ equal. Then we get the equations:

$2x+4y=\mathrm{22.........}\left(1\right)$

$2x-y=\mathrm{2.........}\left(2\right)$

Subtract Equation (2) from Equation (1) to eliminate $x$, because the coefficients of $x$ are the same. So, we get

$(2x-2x)+(4y+y)=22-2$

i.e. $5y=20$

i.e. $y=4$

Substituting this value of $y$ in (2), we get

$2x-4=2$

i.e. $2x=6$

i.e. $x=3$

Hence, the solution of the equations is $x=3,y=4$.