Question

The solution of the pair of linear equations \(x+y=14\) and \(x-y=4\) is _____.

• A. \(9,5\)
• B. \(5,8\)
• C. \(14,4\)
• D. \(8,4\)

Hint:

If coefficients of one variable are opposites like: \[ +y \quad \text{and} \quad -y \] then directly add the equations to eliminate that variable quickly.

Answer 1

The Correct Option is A

Concept: A pair of linear equations can be solved using:
• Substitution Method
• Elimination Method
• Cross Multiplication Method Here the elimination method is easiest because one equation has \(+y\) and the other has \(-y\).

Step 1: Write the equations clearly. \[ x+y=14 \] \[ x-y=4 \]

Step 2: Add both equations. \[ (x+y)+(x-y)=14+4 \] \[ x+y+x-y=18 \]

Step 3: Simplify the equation. \[ 2x=18 \] Divide both sides by 2: \[ x=9 \]

Step 4: Substitute \(x=9\) into one equation. Using: \[ x+y=14 \] Substitute \(x=9\): \[ 9+y=14 \] Subtract 9 from both sides: \[ y=5 \]

Step 5: Verify the solution. Check in second equation: \[ x-y=4 \] Substitute: \[ 9-5=4 \] \[ 4=4 \] Hence the solution is correct. Final Answer: \[ \boxed{(9,5)} \]