The sum of two numbers is 14. The difference of the numbers is 2. What are the numbers
To find the two numbers, let's call them x and y. We can set up two equations based on the information given:
Equation 1: x + y = 14
Equation 2: x - y = 2
To solve this system of equations, we can use the method of substitution or elimination.
Method 1: Substitution
First, isolate one variable in terms of the other using Equation 2:
x = 2 + y
Now substitute this expression for x in Equation 1:
(2 + y) + y = 14
2 + 2y = 14
2y = 14 - 2
2y = 12
y = 12/2
y = 6
Substitute the value of y back into Equation 1 to find x:
x + 6 = 14
x = 14 - 6
x = 8
So the two numbers are x = 8 and y = 6.
Method 2: Elimination
Add the two equations together:
(x + y) + (x - y) = 14 + 2
2x = 16
x = 16/2
x = 8
Substitute the value of x back into either equation to find y:
8 + y = 14
y = 14 - 8
y = 6
Again, the two numbers are x = 8 and y = 6.
x + y = 14
x - y = 2
x = 14 - y
14 - y - y = 2
14 - 2y = 2
-2y = -12
y = 6
x + 6 = 14
x = 8