Question 198292

Start with the given system of equations:


{{{system(7m+n=48,m-6n=13)}}}




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


{{{7m+n=48}}} Start with the first equation



{{{n=48-7m}}}  Subtract {{{7m}}} from both sides



{{{n=-7m+48}}} Rearrange the equation


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Since {{{n=-7m+48}}}, we can now replace each {{{n}}} in the second equation with {{{-7m+48}}} to solve for {{{m}}}




{{{m-6highlight((-7m+48))=13}}} Plug in {{{n=-7m+48}}} into the second equation. In other words, replace each {{{n}}} with {{{-7m+48}}}. Notice we've eliminated the {{{n}}} variables. So we now have a simple equation with one unknown.




{{{m+(-6)(-7)m+(-6)(48)=13}}} Distribute {{{-6}}} to {{{-7m+48}}}



{{{m+42m-288=13}}} Multiply



{{{43m-288=13}}} Combine like terms on the left side



{{{43m=13+288}}}Add 288 to both sides



{{{43m=301}}} Combine like terms on the right side



{{{m=(301)/(43)}}} Divide both sides by 43 to isolate m




{{{m=7}}} Divide






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



So the first part of our answer is: {{{m=7}}}










Since we know that {{{m=7}}} we can plug it into the equation {{{n=-7m+48}}} (remember we previously solved for {{{n}}} in the first equation).




{{{n=-7m+48}}} Start with the equation where {{{n}}} was previously isolated.



{{{n=-7(7)+48}}} Plug in {{{m=7}}}



{{{n=-49+48}}} Multiply



{{{n=-1}}} Combine like terms 




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



So the second part of our answer is: {{{n=-1}}}






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


So our answers are:


{{{m=7}}} and {{{n=-1}}}