Question

Solve following pair of equations by equating the coefficient method:

$2x-y=9$
$3x-7y=19$

• A. $x=2$ , $y=1$
• B. $x=4$ , $y=-1$
• C. $x=3$ , $y=2$
• D. $x=7$ , $y=-8$

Answer 1

Answer: (B)

$x=4$ , $y=-1$

Multiply the equation $2x-y=9$ by $7$ to make the coefficients of $y$ equal. Then we get the equations:

$14x-7y=\mathrm{63.........}\left(1\right)$

$3x-7y=\mathrm{19.........}\left(2\right)$

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

$(14x-3x)+(-7y+7y)=63-19$

i.e. $11x=44$

i.e. $x=4$

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

$12-7y=19$

i.e. $-7y=19-12$

i.e. $-7y=7$

i.e. $y=-1$

Hence, the solution of the equations is $x=4,y=-1$.