If y = 3 and 2x − 5y = 1 are graphed, what is their intersection point?
Answer and explanation
Correct answer: (8, 3)
The governing idea is that the intersection point satisfies both equations simultaneously. Since the first line is y = 3, the y-coordinate of the intersection must be 3. Substitute this value into the second equation: 2x − 5(3) = 1, so 2x − 15 = 1, hence 2x = 16 and x = 8. Therefore the intersection is (8, 3), which is option A. Option B reverses the coordinates. Option C keeps y = 3 but does not satisfy the second equation, since 2(5) − 15 = −5. Options D has the coordinates in an unsuitable order and also fails the fixed y = 3 condition. The horizontal line y = 3 makes the coordinate check especially direct.
Frequently asked questions
What is the correct answer to this question?
(8, 3)
Why is this the correct answer?
The governing idea is that the intersection point satisfies both equations simultaneously. Since the first line is y = 3, the y-coordinate of the intersection must be 3. Substitute this value into the second equation: 2x − 5(3) = 1, so 2x − 15 = 1, hence 2x = 16 and x = 8. Therefore the intersection is (8, 3), which is option A. Option B reverses the coordinates. Option C keeps y = 3 but does not satisfy the second equation, since 2(5) − 15 = −5. Options D has the coordinates in an unsuitable order and also fails the fixed y = 3 condition. The horizontal line y = 3 makes the coordinate check especially direct.
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..
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
