SOLUTION: solve using the addition method 2x+5y=2 3x-2y=3

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Question 147377: solve using the addition method
2x+5y=2
3x-2y=3
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%282x%2B5y=2%2C3x-2y=3%29


-3%282x%2B5y%29=-3%282%29 Multiply the both sides of the first equation by -3.


-6x-15y=-6 Distribute and multiply.


2%283x-2y%29=2%283%29 Multiply the both sides of the second equation by 2.


6x-4y=6 Distribute and multiply.


So we have the new system of equations:
system%28-6x-15y=-6%2C6x-4y=6%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:


%28-6x-15y%29%2B%286x-4y%29=%28-6%29%2B%286%29


%28-6x%2B6x%29%2B%28-15y%2B-4y%29=-6%2B6 Group like terms.


0x%2B-19y=0 Combine like terms. Notice how the x terms cancel out.


-19y=0 Simplify.


y=%280%29%2F%28-19%29 Divide both sides by -19 to isolate y.


y=0 Reduce.


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-6x-15y=-6 Now go back to the first equation.


-6x-15%280%29=-6 Plug in y=0.


-6x%2B0=-6 Multiply.


-6x=-6 Remove any zero terms.


x=%28-6%29%2F%28-6%29 Divide both sides by -6 to isolate x.


x=1 Reduce.


So our answer is x=1 and y=0.


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