Which point does not lie on the line 3x + 8y = 24?
Answer and explanation
Correct answer: (4, 2)
The governing concept is point verification by substitution. A point (x, y) lies on the line 3x + 8y = 24 exactly when its coordinates make the left-hand side equal to 24. For (8, 0), 3(8) + 8(0) = 24. For (0, 3), 3(0) + 8(3) = 24. For (8/3, 2), 3(8/3) + 8(2) = 8 + 16 = 24. However, for (4, 2), 3(4) + 8(2) = 12 + 16 = 28, not 24. Therefore (4, 2) does not lie on the line, making option D correct. The other three points satisfy the equation exactly, so they are valid points on its graph.
Frequently asked questions
What is the correct answer to this question?
(4, 2)
Why is this the correct answer?
The governing concept is point verification by substitution. A point (x, y) lies on the line 3x + 8y = 24 exactly when its coordinates make the left-hand side equal to 24. For (8, 0), 3(8) + 8(0) = 24. For (0, 3), 3(0) + 8(3) = 24. For (8/3, 2), 3(8/3) + 8(2) = 8 + 16 = 24. However, for (4, 2), 3(4) + 8(2) = 12 + 16 = 28, not 24. Therefore (4, 2) does not lie on the line, making option D correct. The other three points satisfy the equation exactly, so they are valid points on its 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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