Question

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

Answer 1

We have:

`</p><p>\begin{cases}</p><p>y=2x+9 \\</p><p>y=-x+6 \\</p><p>\end{cases}</p><p>`

First multiply the second equation by 2 to get:

`</p><p>\begin{cases}</p><p>y=2x+9 \\</p><p>2y=-2x+12 \\</p><p>\end{cases}</p><p>`

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.