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:

Two linear equations represent parallel lines if their slopes are equal but their constants differ.

Answer 1

The Correct Option is B

Rewriting the equations:
\[ 2x + 3y = 4 \quad \cdots (1) \] \[ 4x + 6y = 12 \quad \cdots (2) \] Dividing equation (2) by 2:
\[ 2x + 3y = 6 \] Comparing with equation (1):
\[ 2x + 3y = 4 \] Since both equations have the same left-hand side but different constants on the right-hand side, they represent parallel lines.