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 infinitely many solutions, the condition is:
$\dfrac{a_1}{a_2}
eq\dfrac{b_1}{b_2}$
$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}
eq\dfrac{c_1}{c_2}$
$\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$
$a_1=a_2, b_1=b_2$
Step-by-Step Solution
Key Concept: This is the standard algebraic condition for infinitely many solutions (coincident lines).
Infinitely many solutions occur exactly when $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$. [1.0 Mark]
Correct Answer: $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac{c_1}{c_2}$
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