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From Förberedande kurs i matematik 1

The point of intersection is that point which satisfies the equations of both lines

4x+5y+6=0 and x=0.

Substituting 4x+5y+6=0 into x=0 gives

\displaystyle 4\centerdot 0+5y+6=0\ \Leftrightarrow \ y=-\frac{6}{5}

This gives the point of intersection as \displaystyle \left( 0 \right.,\left. -\frac{6}{5} \right).