Question

Solve elimination 5x+y=9 10x-7y=-18

Answer 1

(1, 4)

To solve this system by addition, notice that if we add these two equations together, neither one of our variables will cancel out.

In this situation, we need to set things up so that when we do add our two equations together, one of the variables will cancel out.

Notice that we have a 10x in our second equation. if we had a -10x in our first equation, then the x's would cancel out.

To create a -10x, we can multiply the top equation by -2 to get a -10x.

From there, rewriting our equation gives us -10x - 2y = -18.

Now the x's cancel. Just add the equations together

now to get the two-step equation -9y = -36.

Solving from here, y = 4.

Now plug y into either one of the equations

to find that x =1.

So our solution is (1,4).