Which point does not lie on the line 2x + 7y = 14?
Answer and explanation
Correct answer: (1, 2)
The governing method is point verification: a point lies on a line exactly when its coordinates satisfy the line equation. For (7, 0), 2(7) + 7(0) = 14, so it lies on the line. For (0, 2), 0 + 14 = 14, so it also lies on the line. For (7/2, 1), 2(7/2) + 7(1) = 7 + 7 = 14, so it lies on the line as well. For (1, 2), 2(1) + 7(2) = 2 + 14 = 16, not 14. Therefore option D is the only point that does not lie on the line. The distinction comes from substitution, not from visual estimation of a graph.
Frequently asked questions
What is the correct answer to this question?
(1, 2)
Why is this the correct answer?
The governing method is point verification: a point lies on a line exactly when its coordinates satisfy the line equation. For (7, 0), 2(7) + 7(0) = 14, so it lies on the line. For (0, 2), 0 + 14 = 14, so it also lies on the line. For (7/2, 1), 2(7/2) + 7(1) = 7 + 7 = 14, so it lies on the line as well. For (1, 2), 2(1) + 7(2) = 2 + 14 = 16, not 14. Therefore option D is the only point that does not lie on the line. The distinction comes from substitution, not from visual estimation of a graph.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Pair of Linear Equations in Two Variables. Topic: Graphical method of finding solutions..
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