SOLUTION: Solve by the substitution method 7m+n=27 m-8n=69

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Question 200627: Solve by the substitution method
7m+n=27
m-8n=69
Found 2 solutions by jim_thompson5910, RAY100:
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%287m%2Bn=27%2Cm-8n=69%29


8%287m%2Bn%29=8%2827%29 Multiply the both sides of the first equation by 8.


56m%2B8n=216 Distribute and multiply.


So we have the new system of equations:
system%2856m%2B8n=216%2Cm-8n=69%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:


%2856m%2B8n%29%2B%28m-8n%29=%28216%29%2B%2869%29


%2856m%2Bm%29%2B%288n-8n%29=216%2B69 Group like terms.


57m%2B0n=285 Combine like terms.


57m=285 Simplify.


m=%28285%29%2F%2857%29 Divide both sides by 57 to isolate m.


m=5 Reduce.


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


56m%2B8n=216 Now go back to the first equation.


56%285%29%2B8n=216 Plug in m=5.


280%2B8n=216 Multiply.


8n=216-280 Subtract 280 from both sides.


8n=-64 Combine like terms on the right side.


n=%28-64%29%2F%288%29 Divide both sides by 8 to isolate n.


n=-8 Reduce.


So the solutions are m=5 and n=-8.


This means that the system is consistent and independent.

Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
(1) 7m +n = 27
(2) m-8n = 69 ,,,,,,,m= (8n +69)
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subst (2) in (1)
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7(8n+69) +n = 27
56n +483 +n = 27
57n = -456
n = -8
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subst in (2) m= (8n +69) = 8(-8) -69 = -64 +69 = 5
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Answer ,,,,,m=5,,,,n=-8
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check
(1) 7(5) +(-8) = 35 -8 = 27,,,,,ok
(2) (5) -8(-8) = 5+64 =69,,,,,,,,ok
.