SOLUTION: The question I need help with is of a systems of equations. Here is the question. y=-x+2 x+2y=6 _______ SOLVE WITH PROCESS OF ELIMINATION PLEASE! Thank u.

Algebra ->  Sequences-and-series -> SOLUTION: The question I need help with is of a systems of equations. Here is the question. y=-x+2 x+2y=6 _______ SOLVE WITH PROCESS OF ELIMINATION PLEASE! Thank u.       Log On


   

Question 169997: The question I need help with is of a systems of equations. Here is the question.

y=-x+2
x+2y=6
_______
SOLVE WITH PROCESS OF ELIMINATION PLEASE!
Thank u.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=-x%2B2 Start with the first equation


x%2By=2 Add "x" to both sides




So we have the system of equations:


system%28x%2By=2%2Cx%2B2y=6%29


-1%28x%2By%29=-1%282%29 Multiply the both sides of the first equation by -1.


-1x-1y=-2 Distribute and multiply.


So we have the new system of equations:
system%28-1x-1y=-2%2Cx%2B2y=6%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:


%28-1x-1y%29%2B%28x%2B2y%29=%28-2%29%2B%286%29


%28-1x%2B1x%29%2B%28-1y%2B2y%29=-2%2B6 Group like terms.


0x%2By=4 Combine like terms. Notice how the x terms cancel out.


y=4 Simplify.


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


-1x-1y=-2 Now go back to the first equation.


-1x-1%284%29=-2 Plug in y=4.


-1x-4=-2 Multiply.


-x=-2%2B4 Add 4 to both sides.


-x=2 Combine like terms on the right side.


x=%282%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-2 Reduce.


So our answer is x=-2 and y=4.


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 y=-x%2B2 (red) and x%2B2y=6 (green)