SOLUTION: -2/3 x + y = 2 2x – 3y = 6 Solve this equation by substitution

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Question 1110715: -2/3 x + y = 2
2x – 3y = 6
Solve this equation by substitution
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
-2/3 x + y = 2
2x – 3y = 6
The first is y=(2/3)x+2
2x-3(2/3)x+3(2)=2
2x-2x-6=2
but this has no solution. Lines are parallel with slope of both (2/3).

Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


To use substitution, you want to solve one of the equations for one of the variables and substitute the expression you get into the other equation.

(1) %28-2%2F3%29x%2By+=+2
(2) +2x-3y+=+6

It looks as if it will be easiest to solve (1) for y:

(1) y+=+%282%2F3%29x%2B2

Now replace "y" in (2) with "(2/3)x+2":

2x-3%28%282%2F3%29x%2B2%29+=+6
2x-2x-6+=+6
-6+=+6

The equation we ended up with is never true; that means the system of equations has no solution.

And in fact the two equations are equations of parallel lines