Question

The solution of the pair of linear equations \( x + y = 10 \), \( x - y = 4 \) is:

• A. \( x = 5, y = 2 \)
• B. \( x = 7, y = 3 \)
• C. \( x = 7, y = -3 \)
• D. \( x = -7, y = -3 \)

Hint:

To solve a system of linear equations, you can add or subtract the equations to eliminate one variable and solve for the other.

Answer 1

The Correct Option is B

We are given the system of linear equations: \[ x + y = 10 \quad \text{(1)} \] \[ x - y = 4 \quad \text{(2)} \]
Step 1: Add the two equations.
Adding equations (1) and (2) eliminates \( y \): \[ (x + y) + (x - y) = 10 + 4 \] \[ 2x = 14 \]
Step 2: Solve for \( x \).
\[ x = \frac{14}{2} = 7 \]
Step 3: Substitute the value of \( x \) into one of the original equations.
Substitute \( x = 7 \) into equation (1): \[ 7 + y = 10 \] \[ y = 10 - 7 = 3 \]
Step 4: Conclusion.
Therefore, the solution of the system is \( x = 7 \) and \( y = 3 \).