Question

Solve the equation using elimination 2x+3y=6. 2x+y=-2

Answer 1

`x=-3`
`y=4`

Explanation:

to use elimination we need to be able eliminate one of the variables.

I will eliminate the x because it looks easier for this problem.

change the signs on the second equation (multiply both sides by -1)

now add the two equations together to eliminate the x

`2x+3y=6`

`-2x-y=2`

`2y=8`

now solve for y by dividing both sides by 2

`y=4`

now that we know y = 4, we can plug this into one of the original equations for y.

I will use the second equation

`2x+(4)=-2`

now solve for x.

subtract 4 from both sides

`2x=-6`

divide both sides by 2

`x=-3`

if you are looking for a coordinate, it is
`(-3,4)`

Hope this helps!

Answer 2

Step 1: Label 2x + 3y = 6 as equation A. Label 2x + y = -2
Step 2: Multiply 2x + y = -2 (equation B) by -1. The new equation, -2x - y = 2 is now equation C
Step 3: Add equation A and C. That will be 2y = 8.
Step 4: Solve for y, which is 4.
Step 5: Plug in the value for y into equation A. 2x + 3(4) = 6.
Step 6: Solve for x, which is -3.