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Pair of Linear Equations in Two Variables

Short Answer Type

71. Find the values of p and q for which the following system of equations has infinite number of solutions. 2x + 3y = 7, (p + q)x + (2p - q)y = 21.

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72. Determine the value of ‘k’ so that the following linear equations have no solution. (3k + 1)x + 3y - 2 = 0, (k² + 1 )x + (k - 2)y - 5 = 0

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73. Determine the values of ‘m’ and ‘n’ so that the following linear equations have infinite solutions (2m - 1)x + 3y - 5 = 0, 3a + (n - 1 )y - 2 = 0

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74. The sum of the numerator and denomi-nator of a fraction is 3 less than twice the denominator. If the numerator and denominator are decreased by 1, the numerator became half the denominator. Determine the fraction.

Solution not provided.

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75. The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator are increased by 3, they are in the ratio 2 : 3. Determine the fraction.

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76. The denominator of a fraction is 4 more than twice the numerator. When both the numerator and denominator are decreased by 6, then the denominator becomes 12 times the numerator. Determine the fraction.

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77. A two-digit number is 4 more than 6 times the sum of its digits. If 18 is subtracted from the number, the digits are reversed. Find the number.

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78. Draw a graph of x - y + 1 = 0 and 3x + 2y - 12 = 0. Calculate the area bounded by these lines and x-axis.

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79. Solve graphically the system of linear equations: 4x - 3y + 4 = 0, 4x + 3y - 20 = 0. Find the area bounded by these lines and x-axis.

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80. Draw the graph of 2x + y = 6 and 2x - y + 2 = 0 Shade the region bounded by these lines and x-axis. Find the area of shaded region.

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