Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
For the pair of linear equations $a_1x+b_1y+c_1=0$ and $a_2x+b_2y+c_2=0$ to have a unique solution, the condition is:
$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}$
$\dfrac{a_1}{a_2}
eq\dfrac{b_1}{b_2}$
$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$
$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}
eq\dfrac{c_1}{c_2}$
Step-by-Step Solution
Key Concept: This is the standard algebraic condition for a unique solution (intersecting lines).
A unique solution occurs exactly when $\dfrac{a_1}{a_2}
eq\dfrac{b_1}{b_2}$. [1.0 Mark]
Correct Answer: $\dfrac{a_1}{a_2}\neq\dfrac{b_1}{b_2}$
Confused by the solution? Ask the AI to explain a specific step, tell you where you went wrong, or break down the key trap in this question.