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 \displaystyle \left( x \right.,\left. y \right), then

\displaystyle y=3x+5

and

\displaystyle y=0 ( \displaystyle x -axis)

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

\displaystyle 0=3x+5 i.e. \displaystyle x=-\frac{5}{3}

The point of intersection is \displaystyle \left( -\frac{5}{3} \right.,\left. 0 \right).