echelon method: 2x + 3y = 10; -3x + 5y =12?

Question

I have not taken a math class in many years and need help passing this one so I can get my degree. I will need a lot of help, it is a 5 week class.

Answer 1

2x + 3y = 10
- 3x + 5y = 12

6x + 9y = 30
- 6x + 10y = 24---------ADD
19y = 54
y = 54 / 19

2x + 162 / 19 = 10
2x = 190 / 19 - 162 / 19
2x = 28 / 19
x = 14 / 19

x = 14 / 19 , y = 54 / 19

Answer 2

The echelon method involves adding equations together to cancel out a coefficient.

Looking out the equations:

2x + 3y = 10
-3x + 5y = 12

Adding them together won't cancel out any coefficients. So let's try cancelling out x's coefficient. Multiply the first equation by 3 and the second equation by 2.

6x + 9y = 30
-6x + 10y = 24

Now adding them together gives:

19y = 54

Now you can solve for y, and plug the value back into one of the original equations to solve for x.