At which point will the lines 5x + 2y = 24 and x - y = 3 meet on the graph?
Answer and explanation
Correct answer: (6, 3)
The intersection point is the ordered pair satisfying both linear equations simultaneously. From x - y = 3, rearrange to y = x - 3. Substitute this expression into 5x + 2y = 24: 5x + 2(x - 3) = 24, so 5x + 2x - 6 = 24, giving 7x = 30, or x = 30/7. Thus the exact intersection is (30/7, 9/7), not any listed option. Therefore the supplied MCQ has no valid correct option; option A, (6,3), gives 36 and 3 in the two equations, so it does not satisfy the first equation. The original key is mathematically incorrect and the item must be revised.
Frequently asked questions
What is the correct answer to this question?
(6, 3)
Why is this the correct answer?
The intersection point is the ordered pair satisfying both linear equations simultaneously. From x - y = 3, rearrange to y = x - 3. Substitute this expression into 5x + 2y = 24: 5x + 2(x - 3) = 24, so 5x + 2x - 6 = 24, giving 7x = 30, or x = 30/7. Thus the exact intersection is (30/7, 9/7), not any listed option. Therefore the supplied MCQ has no valid correct option; option A, (6,3), gives 36 and 3 in the two equations, so it does not satisfy the first equation. The original key is mathematically incorrect and the item must be revised.
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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