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:

$$
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$$

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.