Question
Solve using elimination
3x + y = 10
- 2x + 2y = 12
3x + y = 10
- 2x + 2y = 12
Answers
GPT 3.5
To solve using elimination, we want to adjust the coefficients of one variable so that they add or subtract to eliminate that variable when we add or subtract the equations together.
In this case, if we multiply the first equation by 2, we can get -4x to cancel out with -2x in the second equation.
So,
6x + 2y = 20
- 2x + 2y = 12
When we add these two equations together, we get:
6x + 2y + (-2x + 2y) = 20 + 12
6x - 2x + 2y + 2y = 32
4x + 4y = 32
4(x + y) = 32
(x + y) = 8
So, x + y = 8.
In this case, if we multiply the first equation by 2, we can get -4x to cancel out with -2x in the second equation.
So,
6x + 2y = 20
- 2x + 2y = 12
When we add these two equations together, we get:
6x + 2y + (-2x + 2y) = 20 + 12
6x - 2x + 2y + 2y = 32
4x + 4y = 32
4(x + y) = 32
(x + y) = 8
So, x + y = 8.