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Pair of Linear Equations in Two Variables

Short Answer Type

81. For what value of ‘a’ and ‘b’ the following system of linear equations have an infinite number of solution. 2x + 3y = 7, (a - b)x + (a + b)y 3a + b - 2

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82. Two places A and B are 120 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction, they meet in 6 hours and if they move in opposite directions, they meet in 1 hour 12 minutes. Find the speeds of the cars.

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83. The sum of a two-digit number and the number obtained by reversing the order of its digits is 99. If the digits differ by 3. Find the number.

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84.

Solve the following system of linear equations graphically: 2x - 3y = 1, 3x - 4y = 1 Does the point (3,2) lie on any of the lines? Write its equation.

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85.

Solve the following system of linear equation graphically: 3x - 5y = 19, 3y - 7x - 1 = 0. Does the point (4, 9) lie on any of the lines? Write its equaiton.

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86. For what vlaue of a, the system of linear equation a + 3y = a - 3, 12x + ay a has no solution

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87. For what value of k, the following system of linear equations have (i) a unique solutions, (ii) no solution, 2x + ky = 1, 3x - 5y = 7

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88. Find the values of a and b for which the following system of linear equations has infinite number of solutions: 2x + 3y = 7,(a + b + 1) x + (a + 2b + 2) y = 4 (a + b) + 1

Solution not provided.

Ans. a = 2, b =3

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89. Solve the following system of linear equation graphically: 4x - 5y - 20 = 0, 3x + 5y - 15 = 0. Determine the vertices of the triangle formed by the lines, representing the above equations, and the y-axis.

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90.

Solve the following system of linear equation graphically: 5x - 67 - 30 = 0, 5x + 4y - 20 = 0. Find the vertices of the triangle formed by the above two lines, and x-axis.

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