Question

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

$2x+3y=8$
$2x=2+3y$

• A. $x=3$ and $y=6$
• B. $x=5.5$ and $y=-4$
• C. $x=3$ and $y=2.5$
• D. $x=2.5$ and $y=1$

Answer 1

Answer: (D)

$x=2.5$ and $y=1$

$2x+3y=8$ ...$\left(1\right)$

$2x-3y=2$ ...$\left(2\right)$

Adding $\left(1\right)$ and $\left(2\right)$,

$4x=10$

$x=\frac{1}{4}$ or $x=\frac{5}{2}$

Substituting $x=\frac{5}{2}$ in $\left(1\right)$, we get

$5+3y=8$

$3y=3$

$y=1$

So, $x=\frac{5}{2},y=1$