Point of intersection of 2 Lines

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Find the point of intersection of the lines $9x-y+1=0$ and $7x-y-1=0$.

**Answer**

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

$9x-y+1=0$

$7x-y-1=0$

or,

$63x-7y+7=0$

$63x-9y-9=0$

Subtracting one equation from the other, we get

$2y+16=0$

$y=-8$

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

$9x+8+1= 0$

or, $9x=-9$

or, $x=-1$

The point of intersection is $\left(-1,-8\right)$.