SOLUTION: Addition method 5x-2y=-1 7x+4y=53

Question 218389: Addition method
5x-2y=-1
7x+4y=53
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:

Multiply the both sides of the first equation by 2.

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.

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 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 checkley77(12844) (Show Source): You can put this solution on YOUR website!
5x-2y=-1 multiply by 2 & add
7x+4y=53
10x-4y=-2
------------------
17x=51
x=51/17
x=3 ans.
5*3-2y=-1
15-2y=-1
-2y=-1-15
-2y=-16
y=-16/-2
y=8 ans.
Proof:
7*3+4*8=53
21+32=53
53=53

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