Question

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

$y=4x-7$
$16x-5y=25$

• A. $x=\frac{3}{2},y=6$
• B. $x=\frac{5}{2},y=3$
• C. $x=\frac{7}{4},y=2$
• D. $x=\frac{9}{2},y=0$

Answer 1

The correct option is B $x=\frac{5}{2},y=3$

$4x-y=7$ ...$\left(1\right)$

$16x-5y=25$ ...$\left(2\right)$

Multiplying $\left(1\right)$ by $4$, we get

$16x-4y=28$ ...$\left(3\right)$

$16x-5y=25$ ...$\left(2\right)$

Subtracting $\left(3\right)$ and $\left(2\right)$,

$y=3$

Substituting $y=3$ in $\left(1\right)$, we get $x$ as

$4x-3=7$

$4x=10$

$x=\frac{10}{4}$ or $x=\frac{5}{2}$

$x=\frac{5}{2},y=3$

Option $B$