If y = −2 and 4x + 3y = 10 are graphed, what is their intersection point?
Answer and explanation
Correct answer: (4, −2)
The governing concept is simultaneous satisfaction: an intersection point must lie on both graphs. The equation y = −2 represents a horizontal line, so any common point must have y-coordinate −2. Substitute this value into 4x + 3y = 10: 4x + 3(−2) = 10, giving 4x − 6 = 10, then 4x = 16 and x = 4. Therefore the intersection is (4, −2), so option A is correct. Verification gives 4(4) + 3(−2) = 16 − 6 = 10. Option D has the correct y-coordinate but gives 20 − 6 = 14, not 10. Options B and C do not lie on the horizontal line y = −2.
Frequently asked questions
What is the correct answer to this question?
(4, −2)
Why is this the correct answer?
The governing concept is simultaneous satisfaction: an intersection point must lie on both graphs. The equation y = −2 represents a horizontal line, so any common point must have y-coordinate −2. Substitute this value into 4x + 3y = 10: 4x + 3(−2) = 10, giving 4x − 6 = 10, then 4x = 16 and x = 4. Therefore the intersection is (4, −2), so option A is correct. Verification gives 4(4) + 3(−2) = 16 − 6 = 10. Option D has the correct y-coordinate but gives 20 − 6 = 14, not 10. Options B and C do not lie on the horizontal line y = −2.
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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