Question

The pair of linear equations \( 2x - 3y = 8 \) and \( 4x - 6y = 9 \) are:

• A. Consistent
• B. Inconsistent
• C. Dependent
• D. None of these

Hint:

A system of equations is inconsistent if the lines are parallel, meaning they have the same slope but different intercepts.

Answer 1

The Correct Option is B

Rewriting the equations:
\[ 2x - 3y = 8 \quad \cdots (1) \] \[ 4x - 6y = 9 \quad \cdots (2) \] Step 1: Multiply equation (1) by 2:
\[ 4x - 6y = 16 \] Step 2: Compare with equation (2):
\[ 4x - 6y = 16 \quad \text{(from equation 1)} \] \[ 4x - 6y = 9 \quad \text{(original equation 2)} \] Since the left-hand sides are the same but the right-hand sides are different, the system is inconsistent and has no solution.