Point of intersection of 2 Lines
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Question

Find the point of intersection of the lines $x+y-7=0$ and $7x+y+3=0$.

Answer

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

$x+y-7=0$

$7x+y+3=0$

or,

$7x+7y-49=0$

$7x+y+3=0$

Subtracting one equation from the other, we get

$6y-52=0$

$y=+\frac{26}{3}$

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

$x+\frac{26}{3}-7= 0$

or, $x=-\frac{5}{3}$

The point of intersection is $\left(\frac{-5}{3},\frac{26}{3}\right)$.