Question

1. find the value of two numbers if their sum is 10 and their difference is 2.

Explanation:

Step1: Define variables

Let the two numbers be \( x \) and \( y \), where \( x > y \). We have two equations:

1. \( x + y = 10 \) (sum of the two numbers)
2. \( x - y = 2 \) (difference of the two numbers)

Step2: Solve the system of equations

Add the two equations together:
\[

$$\begin{align*} (x + y) + (x - y) &= 10 + 2 \\ x + y + x - y &= 12 \\ 2x &= 12 \end{align*}$$

\]
Divide both sides by 2:
\[
x = \frac{12}{2} = 6
\]

Step3: Find the value of \( y \)

Substitute \( x = 6 \) into the first equation \( x + y = 10 \):
\[
6 + y = 10
\]
Subtract 6 from both sides:
\[
y = 10 - 6 = 4
\]

Answer:

The two numbers are 6 and 4.