Question 213737
"difference of two numbers is 127" translates to {{{x-y=127}}}


"The larger number is three less than six times the smaller number" means that {{{x=6y-3}}}



{{{x-y=127}}} Start with the first equation.



{{{6y-3-y=127}}} Plug in {{{x=6y-3}}}



{{{5y-3=127}}} Combine like terms on the left side.



{{{5y=127+3}}} Add {{{3}}} to both sides.



{{{5y=130}}} Combine like terms on the right side.



{{{y=(130)/(5)}}} Divide both sides by {{{5}}} to isolate {{{y}}}.



{{{y=26}}} Reduce.



{{{x=6y-3}}} Go back to the second equation.



{{{x=6(26)-3}}} Plug in {{{y=26}}}



{{{x=156-3}}} Multiply



{{{x=153}}} Subtract



So the two numbers are 153 and 26