SOLUTION: The sum of two numbers is 29. Their difference is 7. What are the two numbers

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Question 124692: The sum of two numbers is 29. Their difference is 7. What are the two numbers
Found 2 solutions by gems, jim_thompson5910:
Answer by gems(12) About Me  (Show Source):
You can put this solution on YOUR website!
add the two equations
2x=36
divide both sides by 2
x=18
if x = 18, substitute in the 1st equation x+y=29
18+y=29
y=29-18
y=11
therefore x=18, y=11

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The sentence "The sum of two numbers is 29" translates to the equation x%2By=29


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




Start with the given system of equations:

system%28x%2By=29%2Cx-y=7%29



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%2By=29 Start with the first equation


y=29-x Subtract x from both sides


y=-x%2B29 Rearrange the equation


y=%28-x%2B29%29%2F%281%29 Divide both sides by 1


y=%28%28-1%29%2F%281%29%29x%2B%2829%29%2F%281%29 Break up the fraction


y=-x%2B29 Reduce



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

Since y=-x%2B29, we can now replace each y in the second equation with -x%2B29 to solve for x



x-highlight%28%28-x%2B29%29%29=7 Plug in y=-x%2B29 into the first equation. In other words, replace each y with -x%2B29. Notice we've eliminated the y variables. So we now have a simple equation with one unknown.



x%2Bx-29=7 Distribute the negative


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


2x=7%2B29Add 29 to both sides


2x=36 Combine like terms on the right side


x=%2836%29%2F%282%29 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%2B29 (remember we previously solved for y in the first equation).



y=-x%2B29 Start with the equation where y was previously isolated.


y=-%2818%29%2B29 Plug in x=18


y=-18%2B29 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




So the two numbers are 18 and 11