From Förberedande kurs i matematik 1

According to the definition, the point of intersection between two lines is that point which lies on both lines; it must therefore satisfy the equations of both lines.

If the point of intersection has coordinates (x,y), then

\displaystyle \left\{\begin{align} y&=3x+5\,,\\ y&=0\,\textrm{.}\qquad\quad\text{(x-axis)}\end{align}\right.

If we substitute \displaystyle y=0 into the first equation, we obtain

\displaystyle 0=3x+5,\qquad\text{i.e.}\quad x=-\frac{5}{3}\,\textrm{.}

The point of intersection is (-5/3,0).