SOLUTION: Solve using the elimination method. 2 x - y = 6 5x + y = 22

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Question 243721: Solve using the elimination method.
2 x - y = 6
5x + y = 22
Found 2 solutions by jim_thompson5910, checkley77:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
system%282x-y=6%2C5x%2By=22%29


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


%282x-y%29%2B%285x%2By%29=%286%29%2B%2822%29


%282x%2B5x%29%2B%28-y%2By%29=6%2B22 Group like terms.


7x%2B0y=28 Combine like terms.


7x=28 Simplify.


x=%2828%29%2F%287%29 Divide both sides by 7 to isolate x.


x=4 Reduce.


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


2x-y=6 Now go back to the first equation.


2%284%29-y=6 Plug in x=4.


8-y=6 Multiply.


-y=6-8 Subtract 8 from both sides.


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


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


y=2 Reduce.


So the solutions are x=4 and y=2.


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-y=6 (red) and 5x%2By=22 (green)

Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
2 x - y = 6
5x + y = 22 add.
---------------------
7x=28
x=28/7
x=4 ans.
2*4-y=6
8-y=6
-y=6-8
-y=-2
y=2 ans.
Proof:
5*4+2=22
20+2=22
22=22