Question 118026
Let x=one number (smaller number) and y=another number (larger number)

The sentence "One number is 12 less than another" translates to {{{x=y-12}}} and the sentence "10 times the smaller number minus 2 times the larger number is 8" translates to {{{10x-2y=8}}}


So we get the system 


{{{x=y-12}}}
{{{10x-2y=8}}}



Start with the given system

{{{10x-2y=8}}}
{{{x=y-12}}}




{{{10(y-12)-2y=8}}}  Plug in {{{x=y-12}}} into the first equation. In other words, replace each {{{x}}} with {{{y-12}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{10y-120-2y=8}}} Distribute



{{{8y-120=8}}} Combine like terms on the left side



{{{8y=8+120}}}Add 120 to both sides



{{{8y=128}}} Combine like terms on the right side



{{{y=(128)/(8)}}} Divide both sides by 8 to isolate y




{{{y=16}}} Divide





Now that we know that {{{y=16}}}, we can plug this into {{{x=y-12}}} to find {{{x}}}




{{{x=(16)-12}}} Substitute {{{16}}} for each {{{y}}}



{{{x=4}}} Simplify



So our answer is {{{x=4}}} and {{{y=16}}} which means our numbers are 4 and 16