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Pair of Linear Equations in Two Variables
Previous Year Questions (2022-2024)
Year 2022
- Solve: 2x + 3y = 11, x - 2y = -12.
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From second: x = 2y - 12\nSubstitute: 2(2y-12) + 3y = 11 => 4y - 24 + 3y = 11\n=> 7y = 35 => y = 5\nx = 2(5) - 12 = -2\nSolution: x = -2, y = 5 - A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it goes 40 km upstream and 55 km downstream. Find speed of boat and stream.
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Let speed of boat = x km/h, stream = y km/h\n30x-y + 44x+y = 10\n40x-y + 55x+y = 13\nLet u = 1x-y, v = 1x+y\n30u + 44v = 10\n40u + 55v = 13\nSolving: u = 15, v = 111\nx - y = 5, x + y = 11\nx = 8 km/h, y = 3 km/h
Year 2023
- Solve: 2x + 3y = 11, x - 2y = -12.
Show Solution
From second: x = 2y - 12\nSubstitute: 2(2y-12) + 3y = 11 => 4y - 24 + 3y = 11\n=> 7y = 35 => y = 5\nx = 2(5) - 12 = -2\nSolution: x = -2, y = 5 - A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it goes 40 km upstream and 55 km downstream. Find speed of boat and stream.
Show Solution
Let speed of boat = x km/h, stream = y km/h\n30x-y + 44x+y = 10\n40x-y + 55x+y = 13\nLet u = 1x-y, v = 1x+y\n30u + 44v = 10\n40u + 55v = 13\nSolving: u = 15, v = 111\nx - y = 5, x + y = 11\nx = 8 km/h, y = 3 km/h
Year 2024
- Solve: 2x + 3y = 11, x - 2y = -12.
Show Solution
From second: x = 2y - 12\nSubstitute: 2(2y-12) + 3y = 11 => 4y - 24 + 3y = 11\n=> 7y = 35 => y = 5\nx = 2(5) - 12 = -2\nSolution: x = -2, y = 5 - A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it goes 40 km upstream and 55 km downstream. Find speed of boat and stream.
Show Solution
Let speed of boat = x km/h, stream = y km/h\n30x-y + 44x+y = 10\n40x-y + 55x+y = 13\nLet u = 1x-y, v = 1x+y\n30u + 44v = 10\n40u + 55v = 13\nSolving: u = 15, v = 111\nx - y = 5, x + y = 11\nx = 8 km/h, y = 3 km/h