"Find two numbers whose sum is 81 and whose difference is 35."

Let the two numbers be \( x \) and \( y \).

Given:

1. \( x + y = 81 \) (Their sum is 81)
2. \( x - y = 35 \) (Their difference is 35)

We now have two equations:
1. \( x + y = 81 \)
2. \( x - y = 35 \)

To solve this system of equations, we can add the two equations together:

\[
(x + y) + (x - y) = 81 + 35
\]

Simplifying:

\[
2x = 116
\]

Solving for \( x \):

\[
x = \frac{116}{2} = 58
\]

Now substitute \( x = 58 \) into the first equation \( x + y = 81 \):

\[
58 + y = 81
\]

Solving for \( y \):

\[
y = 81 - 58 = 23
\]

Thus, the two numbers are \( 58 \) and \( 23 \).

Would you like more details on this solution or have any other questions?

Here are 5 related questions to consider:

1. What is the sum and difference of two numbers when given other constraints?
2. How can you use substitution to solve systems of equations?
3. What methods can you use to solve simultaneous equations?
4. Can you derive other relationships between numbers if their sum and difference are known?
5. How do different algebraic techniques simplify solving pairs of equations?

**Tip**: When solving systems of equations, always look for simple operations like addition or subtraction that eliminate one variable.

Find two numbers whose sum is 81 and whose difference is 35.

Learn how to find two numbers whose sum is 81 and whose difference is 35 with this step-by-step algebraic solution. This problem demonstrates solving systems of linear equations and is suitable for students in Grades 6-8.

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