SOLUTION: Solve the given system by use of substitution: 4m+n=26 m-3n=26

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Question 202418: Solve the given system by use of substitution:

4m+n=26
m-3n=26
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%284m%2Bn=26%2Cm-3n=26%29


4m%2Bn=26 Start with the first equation.


n=26-4m Subtract 4m from both sides.


n=-4m%2B26 Rearrange the terms.


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m-3n=26 Move onto the second equation.


m-3%28-4m%2B26%29=26 Now plug in n=-4m%2B26.


m%2B12m-78=26 Distribute.


13m-78=26 Combine like terms on the left side.


13m=26%2B78 Add 78 to both sides.


13m=104 Combine like terms on the right side.


m=%28104%29%2F%2813%29 Divide both sides by 13 to isolate m.


m=8 Reduce.


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Since we know that m=8, we can use this to find n.


4m%2Bn=26 Go back to the first equation.


4%288%29%2Bn=26 Plug in m=8.


32%2Bn=26 Multiply.


n=26-32 Subtract 32 from both sides.


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


So the solutions are m=8 and n=-6.


This means that the system is consistent and independent.