Question

The graphs of the equations \( 2x + 3y = 4 \) and \( 4x + 6y = 12 \) are which type of straight lines?

• A. Coincident straight lines
• B. Parallel straight lines
• C. Intersecting straight lines
• D. None of these

Hint:

If two linear equations have the same coefficients and constants, their graphs represent coincident straight lines, meaning they overlap.

Answer 1

The Correct Option is A

Step 1: Observe the system of equations: \[ 2x + 3y = 4 \quad \text{(1)} \] \[ 4x + 6y = 12 \quad \text{(2)} \] Step 2: Multiply equation (1) by 2: \[ 4x + 6y = 8 \quad \text{(3)} \] Step 3: Compare equation (3) with equation (2): \[ 4x + 6y = 8 \quad \text{and} \quad 4x + 6y = 12 \] These two equations are identical, which means the lines coincide. Thus, the correct answer is coincident straight lines.