Question

The lines \( 2x + 3y - 9 = 0 \) and \( 4x + 6y - 18 = 0 \) are:

• A. intersecting lines
• B. coinciding lines
• C. parallel lines
• D. All of these

Hint:

If one line is a multiple of another, the two lines are coinciding (identical), meaning they lie on top of each other.

Answer 1

The Correct Option is B

Step 1: Compare the two equations.
The given lines are: \[ 2x + 3y - 9 = 0 \quad \text{(Equation 1)} \] \[ 4x + 6y - 18 = 0 \quad \text{(Equation 2)} \] Step 2: Simplify Equation 2.
Observe that Equation 2 is a multiple of Equation 1. We can write Equation 2 as: \[ 4x + 6y - 18 = 2(2x + 3y - 9) \] This shows that Equation 2 is simply twice of Equation 1, meaning both lines are the same. Step 3: Conclusion.
Since the two equations represent the same line, the lines are coinciding lines.