Point of intersection of 2 Lines

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Find the point of intersection of the lines $5x-y-3=0$ and $9x-y+3=0$.

**Answer**

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

$5x-y-3=0$

$9x-y+3=0$

or,

$45x-9y-27=0$

$45x-5y+15=0$

Subtracting one equation from the other, we get

$-4y-42=0$

$y=-\frac{21}{2}$

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

$5x+\frac{21}{2}-3= 0$

or, $5x=-\frac{15}{2}$

or, $x=-\frac{3}{2}$

The point of intersection is $\left(\frac{-3}{2},\frac{-21}{2}\right)$.