NCERT Class 10 Mathematics — The pair of equations $x + 2y

Q: The pair of equations $x + 2y + 5 = 0$ and $-3x - 6y + 1 = 0$ has:

Here $a1 = 1, b1 = 2, c1 = 5$ and $a2 = -3, b2 = -6, c2 = 1$. $\frac{a1}{a2} = \frac{1}{-3} = -\frac{1}{3}$, $\frac{b1}{b2} = \frac{2}{-6} = -\frac{1}{3}$, $\frac{c1}{c2} = \frac{5}{1} = 5$.\nSince $\frac{a1}{a2} = \frac{b1}{b2} \neq \frac{c1}{c2}$, the pair of equations has no solution.

NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesThe pair of equations $x + 2y + 5 = 0$ and $-3x - 6y + 1 = 0$ has:

Step-by-Step Solution

Here $a_1 = 1, b_1 = 2, c_1 = 5$ and $a_2 = -3, b_2 = -6, c_2 = 1$. $\frac{a_1}{a_2} = \frac{1}{-3} = -\frac{1}{3}$, $\frac{b_1}{b_2} = \frac{2}{-6} = -\frac{1}{3}$, $\frac{c_1}{c_2} = \frac{5}{1} = 5$.\nSince $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$, the pair of equations has no solution.

Detailed Options Breakdown

Option : a unique solution

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 1: exactly two solutions

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 2: infinitely many solutions

Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.

Option 3: no solution (Correct Answer)

Correct choice. Refer to the step-by-step verified solution guidelines above for details.

💡 Study Guide: This question tests core syllabus concepts from Pair of Linear Equations in Two Variables. For formulas, key summaries, and mock exam reference guides, read the full Pair of Linear Equations in Two Variables Revision Notes.

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