Point of intersection of 2 Lines

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Find the point of intersection of the lines $8x+y+6=0$ 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

$8x+y+6=0$

$5x+y+4=0$

or,

$40x+5y+30=0$

$40x+8y+32=0$

Subtracting one equation from the other, we get

$-3y-2=0$

$y=-\frac{2}{3}$

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

$8x-\frac{2}{3}+6= 0$

or, $8x=-\frac{16}{3}$

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

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