Question 175696
"one number is equal to two times a second number" translates to {{{x=2y}}}



"Two times the first number plus two times the second number is 24" means that {{{2x+2y=24}}}




So we have the system:


{{{x=2y}}}
{{{2x+2y=24}}}





{{{2(2y)+2y=24}}}  Plug in {{{x=2y}}} into the second equation. In other words, replace each {{{x}}} with {{{2y}}}. Notice we've eliminated the {{{x}}} variables. So we now have a simple equation with one unknown.



{{{4y+2y=24}}} Distribute



{{{6y=24}}} Combine like terms on the left side



{{{y=(24)/(6)}}} Divide both sides by 6 to isolate y



{{{y=4}}} Divide



Now that we know that {{{y=4}}}, we can plug this into {{{x=2y}}} to find {{{x}}}




{{{x=2(4)}}} Substitute {{{4}}} for each {{{y}}}



{{{x=8}}} Multiply



So our answer is {{{x=8}}} and {{{y=4}}} which means that the first number is 8 and the second number is 4.