Point of intersection of 2 Lines

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Find the point of intersection of the lines $5x+y+6=0$ and $5x-y-4=0$.

**Answer**

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

$5x+y+6=0$

$5x-y-4=0$

Subtracting one equation from the other, we get

$2y+10=0$

$y=-5$

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

$5x-5+6= 0$

or, $5x=-1$

or, $x=-\frac{1}{5}$

The point of intersection is $\left(\frac{-1}{5},-5\right)$.