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:

If two linear equations have the same coefficients but different constants, the system is inconsistent and has no solution.

Answer 1

The Correct Option is B

Step 1: Observe the system of equations: \[ 2x - 3y = 8 \quad \text{(1)} \] \[ 4x - 6y = 9 \quad \text{(2)} \] Step 2: Multiply equation (1) by 2: \[ 4x - 6y = 16 \quad \text{(3)} \] Step 3: Compare equation (3) with equation (2): \[ 4x - 6y = 16 \quad \text{and} \quad 4x - 6y = 9 \] These two equations are contradictory, so the system is inconsistent. Thus, the correct answer is inconsistent.