Which point lies on the line 4x − 5y = 0?
Answer and explanation
Correct answer: (5, 4)
A point lies on a line if its coordinates satisfy the equation of that line. Test each candidate by substituting its x- and y-coordinates into 4x − 5y. For (5, 4), the expression is 4(5) − 5(4) = 20 − 20 = 0, so this point satisfies the equation and option B is correct. For (4, 5), the value is 16 − 25 = −9. For (2, 5), it is 8 − 25 = −17, and for (5, 2), it is 20 − 10 = 10. Since none of these values is zero, the other three points do not lie on the line. Direct substitution is the decisive verification method.
Frequently asked questions
What is the correct answer to this question?
(5, 4)
Why is this the correct answer?
A point lies on a line if its coordinates satisfy the equation of that line. Test each candidate by substituting its x- and y-coordinates into 4x − 5y. For (5, 4), the expression is 4(5) − 5(4) = 20 − 20 = 0, so this point satisfies the equation and option B is correct. For (4, 5), the value is 16 − 25 = −9. For (2, 5), it is 8 − 25 = −17, and for (5, 2), it is 20 − 10 = 10. Since none of these values is zero, the other three points do not lie on the line. Direct substitution is the decisive verification method.
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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