SOLUTION: There are two numbers whose sum is 9 and the difference is five . What are the two numbers?

Question 447707: There are two numbers whose sum is 9 and the difference is five . What are the two numbers?
Found 3 solutions by stanbon, solver91311, Leaf W.:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
There are two numbers whose sum is 9 and the difference is five . What are the two numbers?
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Equations:
x + y = 9
x - y = 5
----------------
Add and solve for "x":
2x = 14
x = 7
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Solve for "y":
x + y = 9
7 + y = 9
y = 2
==================
Cheers,
Stan H.
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Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!

Just solve the system. Hint: Already set up to solve by elimination.

John

My calculator said it, I believe it, that settles it

Answer by Leaf W.(135)   (Show Source): You can put this solution on YOUR website!
You can do this two ways: with one variable or with two variables. Personally, I think one variable is easier, but I'll show you both.
1. ONE variable
"two numbers WHOSE SUM IS 9"
x = one number
9 - x = other number (since the sum of the two numbers is 9, and one of them is x, then the other number would be the remainder or the difference when x is subtracted from 9
"the difference is five"
(9 - x) - x = 5
9 - x - x = 5
9 - 2x = 5
Subtract 9 from both sides: -2x = -4
Divide both sides by -2: x = 2
One of the numbers is 2. Plug this into the expression for the other number to find the other number.
9 - x
9 - 2
7
***THEREFORE, THE NUMBERS ARE 2 AND 7.
2. TWO variables
x = one number
y = other number
"whose sum is 9"
x + y = 9
"and the difference is five"
x - y = 5
Solve as a system of equations by "adding" the two equations.
x + y = 9
+(x - y = 5)
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2x + 0y = 14
2x = 14
x = 7
Plug this value for x into either of the two equations and solve for y to find the value of the other number.
x + y = 9
7 + y = 9
y = 2
***THEREFORE, THE NUMBERS ARE TWO AND SEVEN.
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