Point of intersection of 2 Lines

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Find the point of intersection of the lines $10x+y+1=0$ and $4x-y-5=0$.

**Answer**

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

$10x+y+1=0$

$4x-y-5=0$

or,

$20x+2y+2=0$

$20x-5y-25=0$

Subtracting one equation from the other, we get

$7y+27=0$

$y=-\frac{27}{7}$

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

$10x-\frac{27}{7}+1= 0$

or, $10x=\frac{20}{7}$

or, $x=\frac{2}{7}$

The point of intersection is $\left(\frac{2}{7},\frac{-27}{7}\right)$.