SOLUTION: Solve the given system by use of elimination: 5x+2y=-13 7x-3y=17

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Question 202421: Solve the given system by use of elimination:

5x+2y=-13
7x-3y=17
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%2B2y=-13%2C7x-3y=17%29


3%285x%2B2y%29=3%28-13%29 Multiply the both sides of the first equation by 3.


15x%2B6y=-39 Distribute and multiply.


2%287x-3y%29=2%2817%29 Multiply the both sides of the second equation by 2.


14x-6y=34 Distribute and multiply.


So we have the new system of equations:

system%2815x%2B6y=-39%2C14x-6y=34%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:


%2815x%2B6y%29%2B%2814x-6y%29=%28-39%29%2B%2834%29


%2815x%2B14x%29%2B%286y-6y%29=-39%2B34 Group like terms.


29x%2B0y=-5 Combine like terms.


29x=-5 Simplify.


x=%28-5%29%2F%2829%29 Divide both sides by 29 to isolate x.


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15x%2B6y=-39 Now go back to the first equation.


15%28-5%2F29%29%2B6y=-39 Plug in x=-5%2F29.


-75%2F29%2B6y=-39 Multiply.


cross%2829%29%28-75%2Fcross%2829%29%29%2B29%286y%29=29%28-39%29 Multiply EVERY term by the LCD 29 to clear any fractions.


-75%2B174y=-1131 Multiply and simplify.


174y=-1131%2B75 Add 75 to both sides.


174y=-1056 Combine like terms on the right side.


y=%28-1056%29%2F%28174%29 Divide both sides by 174 to isolate y.


y=-176%2F29 Reduce.


So the solutions are x=-5%2F29 and y=-176%2F29.


Which form the ordered pair .


This means that the system is consistent and independent.