We have:
[tex]
\begin{cases}
y=2x+9 \\
y=-x+6 \\
\end{cases}
[/tex]
First multiply the second equation by 2 to get:
[tex]
\begin{cases}
y=2x+9 \\
2y=-2x+12 \\
\end{cases}
[/tex]
Then add the equations to eliminate the x-terms to get:
[tex]3y=21\Longrightarrow y=7[/tex]
And finally use calculated y and plug it in one of the original equations to find x:
[tex]7=6-x\Longrightarrow x=-1[/tex]
The solution is a point [tex]P(-1,7)[/tex] where lines [tex]y=2x+9[/tex] and [tex]y=6-x[/tex] intersect.
Hope this helps.
