Question 110668
Let x=first number, y=second number



So the difference of two numbers is {{{x-y=14}}} (simply subtract the two to get 14). Also, since the "second is less that 2 times the first", this means {{{y=2x-1}}}



So we have the system of equations 

{{{x-y=14}}}
{{{y=2x-1}}}







{{{x-(2x-1)=14}}}  Plug in {{{y=2x-1}}} into the first equation. In other words, replace each {{{y}}} with {{{2x-1}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{x-2x+1=14}}} Distribute the negative



{{{-x+1=14}}} Combine like terms on the left side



{{{-x=14-1}}}Subtract 1 from both sides



{{{-x=13}}} Combine like terms on the right side



{{{x=(13)/(-1)}}} Divide both sides by -1 to isolate x




{{{x=-13}}} Divide





Now that we know that {{{x=-13}}}, we can plug this into {{{y=2x-1}}} to find {{{y}}}




{{{y=2(-13)-1}}} Substitute {{{-13}}} for each {{{x}}}



{{{y=-27}}} Simplify



So our answer is {{{x=-13}}} and {{{y=-27}}}



So our two numbers are -13, -27



Check: Notice if we subtract -27 from -13, we get


{{{-13--27=-13+27=14}}} 


So this verifies our answer



note: with your other answer 15,29, if you subtract, you get: 

{{{15-29=-14}}} which is not what we want