Question

If the sum and difference of two numbers are 8 and 2 respectively, the numbers will be:

• A. 6, 2
• B. 5, 3
• C. 7, 1
• D. 1, 2

Hint:

To solve for two numbers given their sum and difference, add the equations to find one number and subtract to find the other.

Answer 1

The Correct Option is B

Let the two numbers be $x$ and $y$. We are given two equations: \[ x + y = 8 \quad \text{(sum of the numbers)} \] \[ x - y = 2 \quad \text{(difference of the numbers)} \]
Step 1: Solve the system of equations.
Add the two equations: \[ (x + y) + (x - y) = 8 + 2 \] \[ 2x = 10 \] \[ x = 5 \] Substitute $x = 5$ into $x + y = 8$: \[ 5 + y = 8 \] \[ y = 3 \]
Step 2: Conclusion.
The two numbers are $5$ and $3$. Thus, the correct answer is (B) 5, 3.