SOLUTION: how do you solve 5m-2n=4 , 3m+n=9 substitution and elimination

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Question 236474: how do you solve 5m-2n=4 , 3m+n=9 substitution and elimination
Found 2 solutions by jim_thompson5910, JimboP1977:
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%285m-2n=4%2C3m%2Bn=9%29


2%283m%2Bn%29=2%289%29 Multiply the both sides of the second equation by 2.


6m%2B2n=18 Distribute and multiply.


So we have the new system of equations:
system%285m-2n=4%2C6m%2B2n=18%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:


%285m-2n%29%2B%286m%2B2n%29=%284%29%2B%2818%29


%285m%2B6m%29%2B%28-2n%2B2n%29=4%2B18 Group like terms.


11m%2B0n=22 Combine like terms.


11m=22 Simplify.


m=%2822%29%2F%2811%29 Divide both sides by 11 to isolate m.


m=2 Reduce.


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5m-2n=4 Now go back to the first equation.


5%282%29-2n=4 Plug in m=2.


10-2n=4 Multiply.


-2n=4-10 Subtract 10 from both sides.


-2n=-6 Combine like terms on the right side.


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


n=3 Reduce.


So the solutions are m=2 and n=3.

Answer by JimboP1977(311) About Me  (Show Source):
You can put this solution on YOUR website!
5m-2n=4 (equation 1)
3m+n=9 (equation 2)
Multiply (2) by 2 gives
6m+2n=18 (equation 3)
Add equation 3 to 1
11m = 22
So m = 2
You should be able to do the rest from here...