SOLUTION: Solve by the substition method 8m+n=7 m-6n=56

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Question 165293: Solve by the substition method
8m+n=7
m-6n=56
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%288m%2Bn=7%2Cm-6n=56%29



Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for n.




So let's isolate n in the first equation

8m%2Bn=7 Start with the first equation


n=7-8m Subtract 8m from both sides


n=-8m%2B7 Rearrange the equation



---------------------

Since n=-8m%2B7, we can now replace each n in the second equation with -8m%2B7 to solve for m



m-6highlight%28%28-8m%2B7%29%29=56 Plug in n=-8m%2B7 into the second equation. In other words, replace each n with -8m%2B7. Notice we've eliminated the n variables. So we now have a simple equation with one unknown.



m%2B%28-6%29%28-8%29m%2B%28-6%29%287%29=56 Distribute -6 to -8m%2B7


m%2B48m-42=56 Multiply


49m-42=56 Combine like terms on the left side


49m=56%2B42Add 42 to both sides


49m=98 Combine like terms on the right side


m=%2898%29%2F%2849%29 Divide both sides by 49 to isolate m



m=2 Divide





-----------------First Answer------------------------------


So the first part of our answer is: m=2









Since we know that m=2 we can plug it into the equation n=-8m%2B7 (remember we previously solved for n in the first equation).



n=-8m%2B7 Start with the equation where n was previously isolated.


n=-8%282%29%2B7 Plug in m=2


n=-16%2B7 Multiply


n=-9 Combine like terms



-----------------Second Answer------------------------------


So the second part of our answer is: n=-9









-----------------Summary------------------------------

So our answers are:

m=2 and n=-9

which form the point