(1) Solve the following systems of linear equations by Cramer’s rule:
(i) 5x − 2y + 16 = 0, x + 3y − 7 = 0 Solution
(ii) (3/x) + 2y = 12, (2/x) + 3y = 13 Solution
(iii) 3x + 3y − z =11, 2x − y + 2z = 9, 4x + 3y + 2z = 25
(iv) (3/x) - (4/y) - (2/z) - 1 = 0
(1/x) + (2/y) + (1/z) - 2 = 0
(2/x) - (5/y) - (4/z) + 1 = 0 Solution
(2) In a competitive examination, one mark is awarded for every correct answer while 1/4 mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly ? (Use Cramer’s rule to solve the problem)
(3) A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution ? (Use Cramer’s rule to solve the problem). Solution
(4) A fish tank can be filled in 10 minutes using both pumps A and B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30 minutes. How long would it take each pump to fill the tank by itself ? (Use Cramer’s rule to solve the problem).
(5) A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is ₹ 150. The cost of the two dosai, two idlies and four vadais is ₹200. The cost of five dosai, four idlies and two vadais is ₹250. The family has ₹350 in hand and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had ?
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