Choose the correct statement about the graphs of (5x+2y=11) and (10x+3y=21).
Answer and explanation
Correct answer: They will intersect at one point
Compare the ratios of the corresponding coefficients. Here, 5/10 = 1/2, whereas 2/3 is different. Thus, a₁/a₂ ≠ b₁/b₂, so the two lines intersect at exactly one point and the pair has a unique solution. Parallel lines require the first two coefficient ratios to be equal, while coincident lines require all three ratios to be equal. Exam tip: If a₁/a₂ ≠ b₁/b₂, the lines intersect at one point.
Frequently asked questions
What is the correct answer to this question?
They will intersect at one point
Why is this the correct answer?
Compare the ratios of the corresponding coefficients. Here, 5/10 = 1/2, whereas 2/3 is different. Thus, a₁/a₂ ≠ b₁/b₂, so the two lines intersect at exactly one point and the pair has a unique solution. Parallel lines require the first two coefficient ratios to be equal, while coincident lines require all three ratios to be equal. Exam tip: If a₁/a₂ ≠ b₁/b₂, the lines intersect at one point.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Conditions for solvability.
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