Question 124692
The sentence "The sum of two numbers is 29" translates to the equation {{{x+y=29}}}



The sentence "Their difference is 7" translates to the equation {{{x-y=7}}}





Start with the given system of equations:


{{{system(x+y=29,x-y=7)}}}




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=29}}} Start with the first equation



{{{y=29-x}}}  Subtract {{{x}}} from both sides



{{{y=-x+29}}} Rearrange the equation



{{{y=(-x+29)/(1)}}} Divide both sides by {{{1}}}



{{{y=((-1)/(1))x+(29)/(1)}}} Break up the fraction



{{{y=-x+29}}} Reduce




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


Since {{{y=-x+29}}}, we can now replace each {{{y}}} in the second equation with {{{-x+29}}} to solve for {{{x}}}




{{{x-highlight((-x+29))=7}}} Plug in {{{y=-x+29}}} into the first equation. In other words, replace each {{{y}}} with {{{-x+29}}}. Notice we've eliminated the {{{y}}} variables. So we now have a simple equation with one unknown.




{{{x+x-29=7}}} Distribute the negative



{{{2x-29=7}}} Combine like terms on the left side



{{{2x=7+29}}}Add 29 to both sides



{{{2x=36}}} Combine like terms on the right side



{{{x=(36)/(2)}}} Divide both sides by 2 to isolate x




{{{x=18}}} Divide






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



So the first part of our answer is: {{{x=18}}}










Since we know that {{{x=18}}} we can plug it into the equation {{{y=-x+29}}} (remember we previously solved for {{{y}}} in the first equation).




{{{y=-x+29}}} Start with the equation where {{{y}}} was previously isolated.



{{{y=-(18)+29}}} Plug in {{{x=18}}}



{{{y=-18+29}}} Multiply



{{{y=11}}} Combine like terms 




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



So the second part of our answer is: {{{y=11}}}










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


So our answers are:


{{{x=18}}} and {{{y=11}}}


which form the point *[Tex \LARGE \left(18,11\right)] 





So the two numbers are 18 and 11