SOLUTION: I have tried working on this problem for two days so I am giving in to ask for help. Math is NOT my strongest, but my weakest. 2x=2-y 3x+y=-1 I need to solve this by the adiition

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: I have tried working on this problem for two days so I am giving in to ask for help. Math is NOT my strongest, but my weakest. 2x=2-y 3x+y=-1 I need to solve this by the adiition      Log On


   

Question 173076: I have tried working on this problem for two days so I am giving in to ask for help. Math is NOT my strongest, but my weakest. 2x=2-y 3x+y=-1 I need to solve this by the adiition method. I am a student at UOP and do not use a book. I have to use ALEKS which I don't like! Any help would be most appreciated. Thank you in advance, Judy
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2x=2-y Start with the first equation.


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



So we now have the system of equations:
system%282x%2By=2%2C3x%2By=-1%29


-1%282x%2By%29=-1%282%29 Multiply the both sides of the first equation by -1.


-2x-y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-2x-y=-2%2C3x%2By=-1%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28-2x-y%29%2B%283x%2By%29=%28-2%29%2B%28-1%29


%28-2x%2B3x%29%2B%28-y%2By%29=-2%2B-1 Group like terms.


x%2B0y=-3 Combine like terms. Notice how the y terms cancel out.


x=-3 Simplify.


------------------------------------------------------------------


-2x-y=-2 Now go back to the first equation.


-2%28-3%29-y=-2 Plug in x=-3.


6-y=-2 Multiply.


-y=-2-6 Subtract 6 from both sides.


-y=-8 Combine like terms on the right side.


y=%28-8%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=8 Reduce.


So our answer is x=-3 and y=8.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 2x%2By=2 (red) and 3x%2By=-1 (green)