Point of intersection of 2 Lines

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Find the point of intersection of the lines $10x+y+4=0$ and $8x+y+1=0$.

**Answer**

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

$10x+y+4=0$

$8x+y+1=0$

or,

$40x+4y+16=0$

$40x+5y+5=0$

Subtracting one equation from the other, we get

$-y+11=0$

$y=+11$

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

$10x+11+4= 0$

or, $10x=-15$

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

The point of intersection is $\left(\frac{-3}{2},11\right)$.