Question 112245
Translate the following:


"The difference of two problems is 33"---> {{{y-x=33}}}

"The second is 7 less than 3 times the first"---->{{{y=3x-7}}}





Start with the given system

{{{y-x=33}}}
{{{y=3x-7}}}




{{{(3x-7)-x=33}}}  Plug in {{{y=3x-7}}} into the first equation. In other words, replace each {{{y}}} with {{{3x-7}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{2x-7=33}}} Combine like terms on the left side



{{{2x=33+7}}}Add 7 to both sides



{{{2x=40}}} Combine like terms on the right side



{{{x=(40)/(2)}}} Divide both sides by 2 to isolate x




{{{x=20}}} Divide





Now that we know that {{{x=20}}}, we can plug this into {{{y=3x-7}}} to find {{{y}}}




{{{y=3(20)-7}}} Substitute {{{20}}} for each {{{x}}}



{{{y=53}}} Simplify



So our answer is {{{x=20}}} and {{{y=53}}}



So the two numbers are 20 and 53