Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination:$2x+7y=39$, $3x+5y=31$

• A. $x=0,y=7$
• B. $x=6,y=2$
• C. $x=-1,y=3$
• D. $x=2,y=5$

Answer 1

The correct option is D $x=2,y=5$

Multiply the equation $2x+7y=39$ by $3$ and equation $3x+5y=31$ by $2$ to make the coefficients of $x$ equal. Then we get the equations:

$6x+21y=\mathrm{117.........}\left(1\right)$

$6x+10y=\mathrm{62.........}\left(2\right)$

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

$(6x-6x)+(21y-10y)=117-62$

i.e. $11y=55$

i.e. $y=5$

Substituting this value of $y$ in the equation $2x+7y=39$, we get

$2x+35=39$

i.e. $2x=4$

i.e. $x=2$

Hence, the solution of the equations is $x=2,y=5$.