Question

What is the solution to the system of linear equations?
2x+4y=20
3x+2y=26​

Answer 1

We have

`</p><p>\begin{cases}</p><p>2x+4y=20\Longrightarrow x+2y=10\\</p><p>3x+2y=26\\</p><p>\end{cases}</p><p>`

Then multiply the second equation by -1 to get

`</p><p>\begin{cases}</p><p>x+2y=10\\</p><p>-3x-2y=-26\\</p><p>\end{cases}</p><p>`

Now add the equations that way you eliminate y-terms. You find that

`-2x=-16\Longrightarrow x=8`

Now plug in the x to either of the original equations and solve for y.

`</p><p>x+2y=10\\</p><p>8+2y=10\\</p><p>2y=2\Longrightarrow y=1</p><p>`

The solution is the intersection of two lines at
`P(8,1)`.

Hope this helps.