Question

Solve following pair of equations by equating the coefficient method:

$3x-7y=35$
$2x+5y=4$

• A. $x=5,y=-1$
• B. $x=4,y=-1$
• C. $x=5,y=-7$
• D. $x=7,y=-2$

Answer 1

The correct option is D $x=7,y=-2$

Multiply the equation $3x-7y=35$ by $2$ and equation $2x+5y=4$ by $3$ to make the coefficients of $x$ equal. Then we get the equations:

$6x-14y=\mathrm{70.........}\left(1\right)$

$6x+15y=\mathrm{12.........}\left(2\right)$

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

$(6x-6x)+(-14y-15y)=70-12$

i.e. $-29y=58$

i.e. $y=-2$

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

$6x-30=12$

i.e. $6x=42$

i.e. $x=7$

Hence, the solution of the equations is $x=7,y=-2$.