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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
Assertion (A): The graphical method can be used to determine whether a pair of linear equations is consistent or inconsistent. Reason (R): The point of intersection of the two lines gives the solution of the pair of equations, whenever the lines intersect at a unique point.
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: R correctly describes only the intersecting-lines (unique solution) case, but A is a broader statement covering all three cases (intersecting, parallel, coincident) — so R is true but incomplete as an explanation of A.
A is true: by plotting the graphs, one can see whether the lines intersect, are parallel, or coincide, and hence classify the system. [0.5 Mark]
R is also true, but it only explains the unique-solution case; it says nothing about how the graphical method identifies the no-solution (parallel) or infinite-solutions (coincident) cases, so R does not fully explain A. [0.5 Mark]
Correct Answer:Both Assertion (A) and Reason (R) are true, but R is NOT the correct explanation of A.
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