Aus Online Mathematik Brückenkurs 1

At the point where the lines cut each other, we have a point that lies on both lines and which must therefore satisfy the equations of both lines:

\displaystyle x+y+1=0 and \displaystyle x=12.

We obtain the solution to this system of equations by substituting \displaystyle x=12 into the first equation

\displaystyle 12+y+1=0\ \Leftrightarrow \ y=-13

which gives us the point of intersection as \displaystyle \left( 12 \right.,\left. -13 \right).