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

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) (Show Source): You can put this solution on YOUR website!
Start with the first equation.

Add to both sides.

So we now have the system of equations:

Multiply the both sides of the first equation by -1.

Distribute and multiply.

So we have the new system of equations:

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

Group like terms.

Combine like terms. Notice how the y terms cancel out.

Simplify.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

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 (red) and (green)

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