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) (Show Source): You can put this solution on YOUR website!
Start with the given system of equations:
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.
Simplify.
Divide both sides by to isolate .
Reduce.
------------------------------------------------------------------
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 the solutions are 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)
Answer by checkley77(12844) (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
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