The straight lines ${\ell }_1$ and ${\ell }_2$ each pass through the point $(5,4)$. The $y$ intercept of ${\ell }_1$ is $-1$ and the $x$ intercept of ${\ell }_2$ is $13$.

The points $A$ and $B$ lie on the line $y=2$.

Given that $A$ lies on ${\ell }_1$ and $B$ lies on ${\ell }_2$, find the coordinates of $A$ and $B$.

Here is a picture:

You will need to find the equations of ${\ell }_1$ and ${\ell }_2$.