the sum of two numbers is 48 and the difference is 22. What are the numbers?
x + y = 48
x - y = 22
Can you solve these equations?
Ms. Sue, I'm sorry to hijack this question that you answered, but are you able to help me with my precalculus problem?
Sorry -- but precalculus is beyond me.
To find the numbers when their sum and difference are given, you can use a system of equations. Let's assume the numbers as x and y.
Given:
The sum of two numbers is 48 --> x + y = 48
The difference between the two numbers is 22 --> x - y = 22
To solve this system of equations, you can use the method of substitution or elimination.
Method 1: Substitution Method
Solve one equation for one variable and substitute it into the other equation.
Let's solve the first equation for x:
x = 48 - y
Substitute this value of x in the second equation:
(48 - y) - y = 22
48 - 2y = 22
-2y = 22 - 48
-2y = -26
y = (-26)/(-2)
y = 13
Now substitute the value of y in the first equation to find x:
x + 13 = 48
x = 48 - 13
x = 35
Therefore, the two numbers are 35 and 13.
Method 2: Elimination Method
Add or subtract the equations to eliminate one variable.
Let's subtract the second equation from the first equation:
(x + y) - (x - y) = 48 - 22
x + y - x + y = 26
2y = 26
y = 26/2
y = 13
Now substitute the value of y in the first equation to find x:
x + 13 = 48
x = 48 - 13
x = 35
Therefore, the two numbers are 35 and 13.
Both methods yield the same solution, which is x = 35 and y = 13.