Point of intersection of 2 Lines
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Question

Find the point of intersection of the lines $x-y-8=0$ and $x+y-3=0$.

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

$x-y-8=0$

$x+y-3=0$

Subtracting one equation from the other, we get

$-2y-5=0$

$y=-\frac{5}{2}$

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

$x+\frac{5}{2}-8= 0$

or, $x=\frac{11}{2}$

The point of intersection is $\left(\frac{11}{2},\frac{-5}{2}\right)$.