Question 112043
Let x=1st # and y=2nd #


Translate the following:


"The difference of two numbers is 86" becomes {{{x-y=86}}}


"The second is 6 less than 5 times the first" becomes {{{y=5x-6}}}


Start with the given system

{{{x-y=86}}}
{{{y=5x-6}}}




{{{x-(5x-6)=86}}}  Plug in {{{y=5x-6}}} into the first equation. In other words, replace each {{{y}}} with {{{5x-6}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.



{{{x-5x+6=86}}} Distribute the negative



{{{-4x+6=86}}} Combine like terms on the left side



{{{-4x=86-6}}}Subtract 6 from both sides



{{{-4x=80}}} Combine like terms on the right side



{{{x=(80)/(-4)}}} Divide both sides by -4 to isolate x




{{{x=-20}}} Divide





Now that we know that {{{x=-20}}}, we can plug this into {{{y=5x-6}}} to find {{{y}}}




{{{y=5(-20)-6}}} Substitute {{{-20}}} for each {{{x}}}



{{{y=-106}}} Simplify



So our answer is {{{x=-20}}} and {{{y=-106}}}