the sum of two numbers is 90. their difference is 18. Find the numbers.

x + y =90

x-y = 18

Add the two equations together which will eliminate y.

Solve for x and then substitute the value for x into the first equation to find y. check the x and y values in both equations to be sure you are correct.

To find the two numbers, we can solve this problem using a system of linear equations. Let's assign variables to the unknown numbers:

Let's call the first number "x" and the second number "y".

According to the first piece of information, the sum of the two numbers is 90:

x + y = 90 - Equation 1

According to the second piece of information, their difference is 18:

x - y = 18 - Equation 2

Now we have a system of equations. There are several ways to solve this system, but I will use the method of substitution.

1. Solve Equation 2 for x:
x = y + 18

2. Substitute the expression for x in Equation 1:
y + 18 + y = 90

3. Combine like terms:
2y + 18 = 90

4. Subtract 18 from both sides:
2y = 72

5. Divide both sides by 2:
y = 36

Now that we know the value of y, we can substitute it back into one of the original equations to solve for x.

Using Equation 1:
x + 36 = 90

Subtract 36 from both sides:
x = 54

Therefore, the two numbers are 54 and 36.