Paste your question to our Mathbee AI Mentor below to get an instant step-by-step solution.
Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
Assertion (A): The pair of equations $x+2y-4=0$ and $2x+4y-6=0$ has no solution. Reason (R): For this pair, $\dfrac{a_1}{a_2}=\dfrac{b_1}{b_2}=\dfrac12$, but $\dfrac{c_1}{c_2}=\dfrac{-4}{-6}=\dfrac23$, which is not equal to $\dfrac12$.
Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A. Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A. Assertion (A) is true, but Reason (R) is false. Assertion (A) is false, but Reason (R) is true.
Step-by-Step Solution
Key Concept: Direct application of the no-solution condition.
Checking: $\dfrac{1}{2}=\dfrac{2}{4}=\dfrac12$, and $\dfrac{-4}{-6}=\dfrac23 eq\dfrac12$ — this matches the no-solution condition, so A is true. [0.5 Mark]
R correctly computes and compares these exact ratios, which is precisely the justification for A, so R correctly explains A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, and R is the correct explanation of A.
Mathbee AI Mentor (Free Demo)
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.
Master Pair of Linear Equations in Two Variables with Mathbee
Practice this topic under real exam conditions with strict timers, or ask our AI Mentor to explain the concepts step-by-step.