Question

If y=2x+9 and y=6-x what is the solution?

Answer 1

We have:

$\begin{cases}y=2x+9 \\y=-x+6 \\\end{cases}$

First multiply the second equation by 2 to get:

$\begin{cases}y=2x+9 \\2y=-2x+12 \\\end{cases}$

Then add the equations to eliminate the x-terms to get:

$3y=21\Longrightarrow y=7$

And finally use calculated y and plug it in one of the original equations to find x:

$7=6-x\Longrightarrow x=-1$

The solution is a point $P(-1,7)$ where lines $y=2x+9$ and $y=6-x$ intersect.

Hope this helps.