Point of intersection of 2 Lines
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Question

Find the point of intersection of the lines $4x+y+1=0$ and $7x-y+8=0$.

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

$4x+y+1=0$

$7x-y+8=0$

or,

$28x+7y+7=0$

$28x-4y+32=0$

Subtracting one equation from the other, we get

$11y-25=0$

$y=+\frac{25}{11}$

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

$4x+\frac{25}{11}+1= 0$

or, $4x=-\frac{36}{11}$

or, $x=-\frac{9}{11}$

The point of intersection is $\left(\frac{-9}{11},\frac{25}{11}\right)$.