Question 165293


Start with the given system of equations:


{{{system(8m+n=7,m-6n=56)}}}




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+n=7}}} Start with the first equation



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



{{{n=-8m+7}}} Rearrange the equation




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Since {{{n=-8m+7}}}, we can now replace each {{{n}}} in the second equation with {{{-8m+7}}} to solve for {{{m}}}




{{{m-6highlight((-8m+7))=56}}} Plug in {{{n=-8m+7}}} into the second equation. In other words, replace each {{{n}}} with {{{-8m+7}}}. Notice we've eliminated the {{{n}}} variables. So we now have a simple equation with one unknown.




{{{m+(-6)(-8)m+(-6)(7)=56}}} Distribute {{{-6}}} to {{{-8m+7}}}



{{{m+48m-42=56}}} Multiply



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



{{{49m=56+42}}}Add 42 to both sides



{{{49m=98}}} Combine like terms on the right side



{{{m=(98)/(49)}}} 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+7}}} (remember we previously solved for {{{n}}} in the first equation).




{{{n=-8m+7}}} Start with the equation where {{{n}}} was previously isolated.



{{{n=-8(2)+7}}} Plug in {{{m=2}}}



{{{n=-16+7}}} 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 *[Tex \LARGE \left(2,-9\right)]