Question

Solve the following pair of linear (simultaneous) equations by the method of elimination:

$2x+7y=39$
$3x+5y=31$

• A. $x=1,y=6$
• B. $x=7,y=4$
• C. $x=2,y=5$
• D. $x=3,y=1$

Answer 1

Answer: (C)

$x=2,y=5$

$2x+7y=39$ ...$\left(1\right)$

$3x+5y=31$ ...$\left(2\right)$

Multiplying $\left(1\right)$ by $3$ and $\left(2\right)$ by $2$,

$6x+21y=117$ ...$\left(3\right)$

$6x+10y=62$ ...$\left(4\right)$

Subtracting $\left(3\right)$ and $\left(4\right)$,

$11y=55$

$y=5$

Substituting $y=5$ in $\left(1\right)$, we get

$2x+35=39$

$2x=4$

$x=2$

So, $x=2,y=5$

Option $C$