How Do You Solve a System of Equations Using the Elimination by Addition Method?

We're adding these equations together because the -y and +y will cancel out when added together
We used the elimination method to find the value for x, it's 2
We can plug x=2 into our original equations to find the value for y
Our y-value is 2!
Since there is only one solution to this system, we know it's consistent and independent

1. We could use addition, subtraction, or multiplication when using the elimination method
1. The first equation is 2x-y=2
2. The second equation is 2x+y=6
1. We've already done that for you in this example
1. 2x and 2x are like terms, so we can combine them
2. -y and y are also like terms, so we can combine them as well
3. Constants like 6 and 2 are always like terms, so we can combine those also
1. Since we added, the -y and +y canceled out
2. Now dividing both sides by 2 we get x=2
1. We're plugging x=2 into the equations 2x-y=2 and 2x+y=6
1. The first equation was 2x-y=2
1. Multiplying 2•2 gives us 4-y=2
2. Then we can add y to both sides and subtract 2 from both sides to get y=2
1. Let's check to make sure
1. The first equation was 2x+y=6
1. Multiplying 2•2 gives us 4+y=6
2. Subtracting 4 from both sides, we get y=2
1. This means that y is definitely equal to 2

Find the solution to the following system of equations: 2x–y=2 and 2x+y=6