Question

If $(x,y)$ is the point of intersection of the equations $y=\frac{1}{5}x+4$ and $y=\frac{3}{7}x-4$, then find the value of $y$.

• A. $0$
• B. $7$
• C. $10$
• D. $11$

Answer 1

The correct option is D $11$

Given, $y=\frac{1}{5}x+4$

Multiply both side by $5$, we get

$5y=x+20$

$\Rightarrow 5y-x=20...\left(1\right)$

Also given, $y=\frac{3}{7}x-4$

Multiply both sides by $7$, we get

$7y=3x-28$

$\Rightarrow 7y-3x=-28...\left(2\right)$

Multiply equation $\left(1\right)$ by $3$, we get

$15y-3x=60...\left(3\right)$

Subtract equation $\left(2\right)$ with $\left(3\right)$, we get

$8y=88$

$\therefore y=11$