NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 3: Pair of Linear Equations in Two Variables - Exercise 3.1

Question 2

Step 1: Write coefficients.

From the first equation \(x + 2y + 5 = 0\):

\(a_1 = 1,\; b_1 = 2,\; c_1 = 5\).

From the second equation \(-3x - 6y + 1 = 0\):

\(a_2 = -3,\; b_2 = -6,\; c_2 = 1\).

Step 2: Check ratios of coefficients.

\(\dfrac{a_1}{a_2} = \dfrac{1}{-3} = -\dfrac{1}{3}\).

\(\dfrac{b_1}{b_2} = \dfrac{2}{-6} = -\dfrac{1}{3}\).

So, \(\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2}\).

Step 3: Check constant ratio.

\(\dfrac{c_1}{c_2} = \dfrac{5}{1} = 5\).

This is not equal to \(-\dfrac{1}{3}\).

Step 4: Interpret.

Since the first two ratios are equal but different from the third, the lines are parallel and distinct.

Hence, the pair of equations has no solution.