SOLUTION: determine the best method to solve each system of equations. then solve the system. 3x-5y=7 2x+5y=13

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Question 178816: determine the best method to solve each system of equations. then solve the system.
3x-5y=7
2x+5y=13
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Elimination is the easiest way to solve this system.





Start with the given system of equations:
system%283x-5y=7%2C2x%2B5y=13%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%283x-5y%29%2B%282x%2B5y%29=%287%29%2B%2813%29


%283x%2B2x%29%2B%28-5y%2B5y%29=7%2B13 Group like terms.


5x%2B0y=20 Combine like terms.


5x=20 Simplify.


x=%2820%29%2F%285%29 Divide both sides by 5 to isolate x.


x=4 Reduce.


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3x-5y=7 Now go back to the first equation.


3%284%29-5y=7 Plug in x=4.


12-5y=7 Multiply.


-5y=7-12 Subtract 12 from both sides.


-5y=-5 Combine like terms on the right side.


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


y=1 Reduce.


So our answer is x=4 and y=1.


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 3x-5y=7 (red) and 2x%2B5y=13 (green)