Match each pair of boundary lines in List-I with the corner point where they meet in List-II.
| List-I | List-II | ||
|---|---|---|---|
| Pair of lines | Corner point | ||
| (A) | \(x + y = 7\) and \(x - y = 1\) | (I) | \((3, 4)\) |
| (B) | \(2x + y = 10\) and \(x + 2y = 11\) | (II) | \((2, 3)\) |
| (C) | \(x + 2y = 12\) and \(3x - y = 8\) | (III) | \((4, 3)\) |
| (D) | \(x + 4y = 14\) and \(2x + y = 7\) | (IV) | \((4, 4)\) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(I), (C)-(IV), (D)-(II)
A corner point is the point where two boundary lines meet, so each pair of equations is solved together.
(A) \(x + y = 7\) and \(x - y = 1\)
Adding: \(2x = 8\), so \(x = 4, \; y = 3\)
This matches (III) (4, 3).
(B) \(2x + y = 10\) and \(x + 2y = 11\)
Adding: \(3x + 3y = 21\), so \(x + y = 7\)
Subtracting: \(x - y = -1\), so \(x = 3, \; y = 4\)
This matches (I) (3, 4).
(C) \(x + 2y = 12\) and \(3x - y = 8\)
\(y = 3x - 8\)
\(x + 6x - 16 = 12\), so \(x = 4, \; y = 4\)
This matches (IV) (4, 4).
(D) \(x + 4y = 14\) and \(2x + y = 7\)
\(y = 7 - 2x\)
\(x + 28 - 8x = 14\), so \(x = 2, \; y = 3\)
This matches (II) (2, 3).