Point of intersection of 2 Lines
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Question

Find the point of intersection of the lines $9x-y+8=0$ and $7x-y-10=0$.

Answer

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

$9x-y+8=0$

$7x-y-10=0$

or,

$63x-7y+56=0$

$63x-9y-90=0$

Subtracting one equation from the other, we get

$2y+146=0$

$y=-73$

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

$9x+73+8= 0$

or, $9x=-81$

or, $x=-9$

The point of intersection is $\left(-9,-73\right)$.