Point of intersection of 2 Lines
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Question

Find the point of intersection of the lines $8x-y+7=0$ and $2x-y+4=0$.

Answer

If the point $P(x,y)$ is the point of intersection, the coordinates $x$ and $y$ must satisfy the two equations

$8x-y+7=0$

$2x-y+4=0$

or,

$8x-y+7=0$

$8x-4y+16=0$

Subtracting one equation from the other, we get

$3y-9=0$

$y=+3$

Substituting the value of $y$ in the first equation, we get

$8x-3+7= 0$

or, $8x=-4$

or, $x=-\frac{1}{2}$

The point of intersection is $\left(\frac{-1}{2},3\right)$.