Question

Solve the pair of linear equations \( 2x + 3y = 11 \) and \( 2x - 4y = -24 \) using the substitution or elimination method.

Hint:

If the coefficients of one variable are already equal, subtract the equations directly to eliminate that variable quickly.

Answer 1

Concept: A pair of linear equations can be solved using:

• Substitution method
• Elimination method

Here, we use the elimination method to remove one variable.
Step 1: Write the given equations.
\[ (1)\; 2x + 3y = 11 \] \[ (2)\; 2x - 4y = -24 \]
Step 2: Eliminate \( x \) by subtraction.
Subtract equation (2) from equation (1): \[ (2x + 3y) - (2x - 4y) = 11 - (-24) \] \[ 2x + 3y - 2x + 4y = 35 \] \[ 7y = 35 \]
Step 3: Solve for \( y \).
\[ y = \frac{35}{7} = 5. \]
Step 4: Substitute \( y = 5 \) into equation (1).
\[ 2x + 3(5) = 11 \] \[ 2x + 15 = 11 \] \[ 2x = -4 \] \[ x = -2. \] Conclusion:
The solution of the pair of linear equations is: \[ x = -2, \quad y = 5. \] Note: The computed values satisfy both equations.