Question 202418


Start with the given system of equations:



{{{system(4m+n=26,m-3n=26)}}}



{{{4m+n=26}}} Start with the first equation.



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



{{{n=-4m+26}}} Rearrange the terms.



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



{{{m-3(-4m+26)=26}}} Now plug in {{{n=-4m+26}}}.



{{{m+12m-78=26}}} Distribute.



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



{{{13m=26+78}}} Add {{{78}}} to both sides.



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



{{{m=(104)/(13)}}} 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+n=26}}} Go back to the first equation.



{{{4(8)+n=26}}} Plug in {{{m=8}}}.



{{{32+n=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.