Question

The graphs of the equations \( 2x + 3y + 15 = 0 \) and \( 3x - 2y - 12 = 0 \) are:

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

Hint:

Two linear equations intersect if their ratios of coefficients are not equal.

Answer 1

The Correct Option is C

Comparing coefficients:
\[ \frac{a_1}{a_2} = \frac{2}{3}, \quad \frac{b_1}{b_2} = \frac{3}{-2}. \] Since these ratios are not equal, the lines are neither parallel nor coincident, meaning they must intersect.