Question 119835
You can solve this two ways.
4x+3y=-2
5x+7y=17

I am going to cancel or eliminate the x's. To do this multiply both problems by a number to get the x's the same, but one positive and one negative.
5(4x+3y=-2)
-4(5x+7y=17)
You then get 20x+15y=-10
             -20x-28y=-68
You subtract or add and the x's cancel or eliminate.You get -13y=-78.You divide both sides by -13 and get y=6.To get the solution for x, you plug y=6 into the original problem.
TO plug in 6, do the following
4x+3(6)=-2 which gives you 4x+18=-2.
You subtract 18 to both sides which gives you 4x=-20. YOu divide by 4 on both sides and get x=-5.


To plug in y=6 into 5x+7y=17, do the following.
5x+7(6)=17 which gives you 5x+42=17.
You subtract 42 from both sides and get 5x=-25.
You divide both sides by 5 and get x=-5
The answer is(-5,6).




THe other way to do the problems is to eliminate the y's.
4x+3y=-2
5x+7y=17


-7(4x+3y=-2)
3(5x+7y=17)
This gives you the following:
-28x-21y=14
15x+21y=51
The y's cancel or eliminate and gives you -13x=65. You divide both sides by -13 and it gives you x=-5.
Plug x=-5 back into either problem and get the solution for y. You shoud get the same answer as above which is (-5,6).