Pair of Linear Equations in Two Variables

⭐ Important Questions

1. 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
2. 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