SOLUTION: please help. The sum if two numbers is 35. Their difference is 13. what are the two numbers?

Question 81569: please help.
The sum if two numbers is 35. Their difference is 13. what are the two numbers?
Found 2 solutions by tutorcecilia, tutor_paul:
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
x=one number
y=the other number
sum=to add
difference=to subtract
.
x+y=35
x-y=12
.
One method you can use is subtraction;
x+y=35
x-y=12
_______
2x-0y=47
.
2x=47
x=47/2
.
So, x=47/2=23.5
x+y=35
23.5+y=35
y=35-23.5
y=11.5
checking: 23.5+11.5=35
.
Plug the values into the second equation:
x-y=12
23.5-11.5=12 [checks out]

Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
You are given two equations and two unknowns. Anytime you have at least as many equations as you have unknowns, you can solve the problem!
=================================
Let the two numbers in question be called x and y.
From the given information we can say:
Equation #1:
and
Equation #2:
So, you have 2 equations and 2 unknowns. you are good to go.
==================================
First, Solve Equation #2 for x in terms of y:

Now, substitute this expression for x into Equation #1 (that is why this is called the "substitution" method.

Solve for y:

Now, substitute this value for y back in to Equation #2:

Solve for x:

Check these answers by plugging the values back in to the original equations. They should both hold true.
Good Luck,
tutor_paul@yahoo.com
RELATED QUESTIONS
The sum if two numbers is 35. Their difference is 9. what are the two... (answered by macston)
The sum of two numbers is 65 and their difference is 13. what are the... (answered by Edwin McCravy)
The sum of two numbers is 155, while the difference of the two numbers is 35. What are... (answered by Alan3354)
The sum of two numbers is 30. Their difference is 6. What are the two... (answered by checkley71)
The sum of two numbers is 34. Their difference is 10. What are the two... (answered by stanbon,atif.muhammad,tutorcecilia)
The sum of two numbers is 39. Their difference is 11. What are the two... (answered by consc198)
The sum of two numbers is 33. Their difference is 11. What are the two... (answered by praseenakos@yahoo.com)
The sum of two numbers is 29. Their difference is 7. What are the two... (answered by uma)
The sum of two numbers is 29. Their difference is 7. What are the two... (answered by checkley71)