Question

Solve the following pairs of linear (simultaneous) equation by the method of elimination:$y=4x-7$, $16x-5y=25$

• A. $x=\frac{7}{5},y=10$
• B. $x=\frac{5}{2},y=3$
• C. $x=\frac{1}{2},y=4$
• D. $x=\frac{9}{2},y=8$

Answer 1

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

The equation $y=4x-7$ can be rewritten as $4x-y=7$ and multiply the equation $4x-y=7$ by $4$. Then we get the following equations:

$16x-5y=\mathrm{25.........}\left(1\right)$

$16x-4y=\mathrm{28.........}\left(2\right)$

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

$(16x-16x)+(-4y+5y)=28-25$

i.e. $y=3$

Substituting this value of $y$ in the equation $4x-y=7$, we get

$4x-3=7$

i.e. $4x=10$

i.e. $x=\frac{5}{2}$

Hence, the solution of the equations is $x=\frac{5}{2},y=3$.