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

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Question 218389: Addition method
5x-2y=-1
7x+4y=53
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%285x-2y=-1%2C7x%2B4y=53%29


2%285x-2y%29=2%28-1%29 Multiply the both sides of the first equation by 2.


10x-4y=-2 Distribute and multiply.


So we have the new system of equations:
system%2810x-4y=-2%2C7x%2B4y=53%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:


%2810x-4y%29%2B%287x%2B4y%29=%28-2%29%2B%2853%29


%2810x%2B7x%29%2B%28-4y%2B4y%29=-2%2B53 Group like terms.


17x%2B0y=51 Combine like terms. Notice how the y terms cancel out.


17x=51 Simplify.


x=%2851%29%2F%2817%29 Divide both sides by 17 to isolate x.


x=3 Reduce.


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


10x-4y=-2 Now go back to the first equation.


10%283%29-4y=-2 Plug in x=3.


30-4y=-2 Multiply.


-4y=-2-30 Subtract 30 from both sides.


-4y=-32 Combine like terms on the right side.


y=%28-32%29%2F%28-4%29 Divide both sides by -4 to isolate y.


y=8 Reduce.


So our answer is x=3 and y=8.


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 5x-2y=-1 (red) and 7x%2B4y=53 (green)

Answer by checkley77(12844) About Me  (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