Question 202006
"The sum of two numbers is 22" translates to {{{x+y=22}}}


"the larger number is subtracted from three times the smaller the difference is 6" translates to {{{3x-y=6}}}





Start with the given system of equations:

{{{system(x+y=22,3x-y=6)}}}



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



{{{(x+y)+(3x-1y)=(22)+(6)}}}



{{{(1x+3x)+(1y+-1y)=22+6}}} Group like terms.



{{{4x+0y=28}}} Combine like terms.



{{{4x=28}}} Simplify.



{{{x=(28)/(4)}}} Divide both sides by {{{4}}} to isolate {{{x}}}.



{{{x=7}}} Reduce.



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{{{x+y=22}}} Now go back to the first equation.



{{{7+y=22}}} Plug in {{{x=7}}}.



{{{7+y=22}}} Multiply.



{{{y=22-7}}} Subtract {{{7}}} from both sides.



{{{y=15}}} Combine like terms on the right side.



So the solutions are {{{x=7}}} and {{{y=15}}}.



So the larger number is 15 and the smaller number is 7.