Question 124657
The sentence "The sum of two numbers is 38" translates to the equation {{{x+y=38}}}




The sentence "Their difference is 10" translates to the equation  {{{x-y=10}}}





Start with the given system of equations:


{{{system(x+y=38,x-y=10)}}}




Now in order to solve this system by using substitution, we need to solve (or isolate) one variable. I'm going to solve for y.





So let's isolate y in the first equation


{{{x+y=38}}} Start with the first equation



{{{y=38-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+38}}} Rearrange the equation



{{{y=(-x+38)/(1)}}} Divide both sides by {{{1}}}



{{{y=((-1)/(1))x+(38)/(1)}}} Break up the fraction



{{{y=-x+38}}} Reduce




---------------------


Since {{{y=-x+38}}}, we can now replace each {{{y}}} in the second equation with {{{-x+38}}} to solve for {{{x}}}




{{{x-highlight((-x+38))=10}}} Plug in {{{y=-x+38}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+38}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+x-38=10}}} Distribute the negative



{{{2x-38=10}}} Combine like terms on the left side



{{{2x=10+38}}}Add 38 to both sides



{{{2x=48}}} Combine like terms on the right side



{{{x=(48)/(2)}}} Divide both sides by 2 to isolate x




{{{x=24}}} Divide






-----------------First Answer------------------------------



So the first part of our answer is: {{{x=24}}}










Since we know that {{{x=24}}} we can plug it into the equation {{{y=-x+38}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+38}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(24)+38}}} Plug in {{{x=24}}}



{{{y=-24+38}}} Multiply



{{{y=14}}} Combine like terms 




-----------------Second Answer------------------------------



So the second part of our answer is: {{{y=14}}}










-----------------Summary------------------------------


So our answers are:


{{{x=24}}} and {{{y=14}}}


which form the point *[Tex \LARGE \left(24,14\right)] 





So the two numbers are 24 and 14