Question 93010
{{{x-y=27}}} "The difference of two numbers is 27"


{{{y=3x-1}}} "The second is 1 less than 3 times the first"


{{{x-(3x-1)=27}}} Plug in {{{y=3x-1}}}


{{{x-3x+1=27}}}  Distribute



{{{-2x+1=27}}}  Combine the variable terms 1x and  -3x  on the left side to get -2x




{{{-2x=27-1}}} Subtract 1 from both sides





{{{-2 x=26}}} Combine like terms -1 and 27 on the right side to get 26






{{{x=(26)/(-2)}}} Now divide both sides by  -2 to isolate and solve for x



{{{x= -13}}} Reduce




So our answer is

{{{x= -13}}}



Plug in {{{x= -13}}} to find y



{{{y=3(-13)-1}}}


{{{y=-39-1}}}


{{{y=-40}}}



So the two numbers are -13 and -40


=====================================


Check:


{{{-13 --40=27}}}  Plug in x=-13 and y=-40


{{{27=27}}} works