SOLUTION: Solve the system by addition: x-y = -1 5x+2y = 30

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Question 376337: Solve the system by addition:
x-y = -1
5x+2y = 30
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%28x-y=-1%2C5x%2B2y=30%29


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


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


So we have the new system of equations:
system%282x-2y=-2%2C5x%2B2y=30%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:


%282x-2y%29%2B%285x%2B2y%29=%28-2%29%2B%2830%29


%282x%2B5x%29%2B%28-2y%2B2y%29=-2%2B30 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.


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


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


8-2y=-2 Multiply.


-2y=-2-8 Subtract 8 from both sides.


-2y=-10 Combine like terms on the right side.


y=%28-10%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=5 Reduce.


So the solutions are x=4 and y=5.


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 x-y=-1 (red) and 5x%2B2y=30 (green)


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim