Question 175702


Start with the given system of equations:

{{{system(2r+2s=50,2r-s=17)}}}



{{{2(2r-s)=2(17)}}} Multiply the both sides of the second equation by 2.



{{{4r-2s=34}}} Distribute and multiply.



So we have the new system of equations:

{{{system(2r+2s=50,4r-2s=34)}}}



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



{{{(2r+2s)+(4r-2s)=(50)+(34)}}}



{{{(2r+4r)+(2s+-2s)=50+34}}} Group like terms.



{{{6r+0s=84}}} Combine like terms.



{{{6r=84}}} Simplify.



{{{r=(84)/(6)}}} Divide both sides by {{{6}}} to isolate {{{r}}}.



{{{r=14}}} Reduce.



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{{{2r+2s=50}}} Now go back to the first equation.



{{{2(14)+2s=50}}} Plug in {{{r=14}}}.



{{{28+2s=50}}} Multiply.



{{{2s=50-28}}} Subtract {{{28}}} from both sides.



{{{2s=22}}} Combine like terms on the right side.



{{{s=(22)/(2)}}} Divide both sides by {{{2}}} to isolate {{{s}}}.



{{{s=11}}} Reduce.



So our answer is {{{r=14}}} and {{{s=11}}}.



This means that the system is consistent and independent.