SOLUTION: Solve the system by the elimination method. 5x+5y=-13 7x-2y=19

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Question 238564: Solve the system by the elimination method.
5x+5y=-13
7x-2y=19
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%2B5y=-13%2C7x-2y=19%29


2%285x%2B5y%29=2%28-13%29 Multiply the both sides of the first equation by 2.


10x%2B10y=-26 Distribute and multiply.


5%287x-2y%29=5%2819%29 Multiply the both sides of the second equation by 5.


35x-10y=95 Distribute and multiply.


So we have the new system of equations:
system%2810x%2B10y=-26%2C35x-10y=95%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%2B10y%29%2B%2835x-10y%29=%28-26%29%2B%2895%29


%2810x%2B35x%29%2B%2810y%2B-10y%29=-26%2B95 Group like terms.


45x%2B0y=69 Combine like terms.


45x=69 Simplify.


x=%2869%29%2F%2845%29 Divide both sides by 45 to isolate x.


x=23%2F15 Reduce.


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10x%2B10y=-26 Now go back to the first equation.


10%2823%2F15%29%2B10y=-26 Plug in x=23%2F15.


46%2F3%2B10y=-26 Multiply.


3%2846%2Fcross%283%29%2B10y%29=3%28-26%29 Multiply both sides by the LCD 3 to clear any fractions.


46%2B30y=-78 Distribute and multiply.


30y=-78-46 Subtract 46 from both sides.


30y=-124 Combine like terms on the right side.


y=%28-124%29%2F%2830%29 Divide both sides by 30 to isolate y.


y=-62%2F15 Reduce.


So the solutions are x=23%2F15 and y=-62%2F15.


Which form the ordered pair .


This means that the system is consistent and independent.