NCERT · Class 10 · Mathematics · Pair of Linear Equations in Two VariablesIf a pair of linear equations $a1x + b1y + c1 = 0$ and $a2x + b2y + c2 = 0$ has a unique solution, then which of the following conditions is correct?
Step-by-Step Solution
For a pair of linear equations to have a unique solution, the ratio of the coefficients of $x$ and $y$ must not be equal, i.e., $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$.
Detailed Options Breakdown
Option : $\frac{a_1}{a_2} \neq \frac{b_1}{b_2}$ (Correct Answer)
Correct choice. Refer to the step-by-step verified solution guidelines above for details.
Option 1: $\frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
Option 2: $\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
Option 3: $\frac{a_1}{a_2} \neq \frac{c_1}{c_2}$
Incorrect choice. This distractor represents a common misunderstanding of the core principles of Pair of Linear Equations in Two Variables.
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