Question 176235
{{{5c+b=11}}} Start with the second equation.



{{{b+5c=11}}} Rearrange the terms.





Start with the given system of equations:

{{{system(3b+2c=46,b+5c=11)}}}



{{{-3(b+5c)=-3(11)}}} Multiply the both sides of the second equation by -3.



{{{-3b-15c=-33}}} Distribute and multiply.



So we have the new system of equations:

{{{system(3b+2c=46,-3b-15c=-33)}}}



Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:



{{{(3b+2c)+(-3b-15c)=(46)+(-33)}}}



{{{(3b+-3b)+(2c+-15c)=46+-33}}} Group like terms.



{{{0b+-13c=13}}} Combine like terms.



{{{-13c=13}}} Simplify.



{{{c=(13)/(-13)}}} Divide both sides by {{{-13}}} to isolate {{{c}}}.



{{{c=-1}}} Reduce.



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{{{3b+2c=46}}} Now go back to the first equation.



{{{3b+2(-1)=46}}} Plug in {{{c=-1}}}.



{{{3b-2=46}}} Multiply.



{{{3b=46+2}}} Add {{{2}}} to both sides.



{{{3b=48}}} Combine like terms on the right side.



{{{b=(48)/(3)}}} Divide both sides by {{{3}}} to isolate {{{b}}}.



{{{b=16}}} Reduce.



So our answer is {{{b=16}}} and {{{c=-1}}}.



This means that the system is consistent and independent.