How to find the point of intersection of two lines?
By Emma Johnson •
How to find the point of intersection of two lines ?
Let's say $2x+y=5$ and $3x+2y=5$ ?
Thanks
$\endgroup$ 11 Answer
$\begingroup$The graphs of two lines intersect at a point $(s,t)$ when the point $(s,t)$ is on both lines.
The point $(s,t)$ lies on the line $ax+by=c$ when $as+bt=c$.
Thus, to find the intersection of two lines $ax+by=c$ and $dx+ey=f$ (if it exists), we want to look for a pair of numbers $s$ and $t$ for which $$as+bt=c\qquad\text{and}\qquad ds+et=f.$$
In your example, we want to find an $s$ and $t$ for which $2s+t=5$ and $3s+2t=5$.
Note that if $2s+t=5$, then $t=5-2s$. Substitute this in for $t$ in the expression $3s+2t=5$ to find the value for $s$. Then solve for $t$ using the fact that $t=5-2s$.
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