SOLUTION: Solve using the elimination method. 2x

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Question 170660This question is from textbook Introductory Algebra
: Solve using the elimination method.
2x - y = 6
5x + y = 22 This question is from textbook Introductory Algebra

Found 2 solutions by jim_thompson5910, Mathtut:
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. Notice how the y terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

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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)

Answer by Mathtut(3670) (Show Source):
You can put this solution on YOUR website!
2x-y=6....eq 1
5x+y=22...eq 2
:
this problem is already set up nicely without having to multiply either equation by anything. Just add eq1 to eq 2 and the y terms will be eliminated.
:
we are left with
the x terms 2x+5x and the constants 6+22
:
2x+5x=6+22
:
7x=28
:

now substitute x's value back into either equation....I will use eq 2
:
5(4)+y=22---->20+y=22--->subtraction 20 frome each side produces

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