SOLUTION: -6x-4y=18 4y=-6x-18 & 2x+2y=2 Y=3-3x Hello, I am trying to find the solution for the system of equations..please help. Ty

Algebra ->  Inequalities -> SOLUTION: -6x-4y=18 4y=-6x-18 & 2x+2y=2 Y=3-3x Hello, I am trying to find the solution for the system of equations..please help. Ty      Log On


   

Question 760423: -6x-4y=18
4y=-6x-18
&
2x+2y=2
Y=3-3x
Hello, I am trying to find the solution for the system of equations..please help. Ty
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Those equations are begging to get simplified and rearranged into an equivalent, simple, more standard form.
-6x-4y=18 --> 6x%2B4y=-18 --> 3x%2B2y=-9 (multiplying both sides of the equal sign times (-1) and then dividing by 2 both sides of the equal sign )
4y=-6x-18 --> 6x%2B4y=-18 --> Wait. I do not need to go further. Both equations are equivalent to 6x%2B4y=-18.
They both represent the same line. There is an infinite number of (x,y) pairs that satisfy both equations:all the points on the line 6x%2B4y=-18.

The equations in the next system represent lines that are not the same and are not parallel, so there is a unique (x,y) pair that is the solution of the system:
2x%2B2y=2 --> x%2By=1 <--> y=1-x (a line with slope=-1)
y=3-3x (a line with slope=-3)
system%282x%2B2y=2%2Cy=3-3x%29 --> system%28x%2By=1%2Cy=3-3x%29 --> system%28y=1-x%2Cy=3-3x%29 --> system%28y=1-x%2C1-x=3-3x%29 --> system%28y=1-x%2C1%2B2x=3%29 --> system%28y=1-x%2C2x=2%29 --> system%28y=1-x%2Cx=1%29 --> system%28y=1-1%2Cx=1%29 --> highlight%28system%28y=0%2Cx=1%29%29