SOLUTION: How do I solve: x-y=3 -6x+6y=17 and: 2x=2-y 3x+y=-1

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Question 283897: How do I solve:
x-y=3
-6x+6y=17
and:
2x=2-y
3x+y=-1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first to get you started.

# 1

The goal to solving systems of equations is to eliminate one variable so you can solve for the other.


x-y=3 Start with the first equation.


x=3%2By Add 'y' to both sides.


-6x%2B6y=17 Move onto the second equation.


-6%283%2By%29%2B6y=17 Plug in x=3%2By. In other words, replace each 'x' with '3+y' (since they are equal).


Notice how the 'x' terms are now gone and we're just left with one variable 'y'. We can now solve for 'y'.


-18-6y%2B6y=17 Distribute.


-18%2B0y=17 Combine like terms.


-18=17 Simplify.


Since the equation -18=17 is NEVER true (regardless of the value of 'y'), this means that there are NO solutions (in terms of 'y').


Consequently, this means that there are NO solutions in terms of 'x' as well.


So there are NO solutions. This means that the system is inconsistent.