(1) Which of the following pairs of linear equations has unique solution, no solution, infinitely many solutions. In case there is unique solution, find it by using cross multiplication method.
(i) x – 3y – 3 = 0 and 3x – 9y – 2 = 0 Solution
(ii) 2x + y = 5 and 3x + 2y = 8 Solution
(iii) 3x – 5y = 20 and 6x – 10y = 40 Solution
(iv) x – 3y – 7 = 0 and 3x – 3y – 15 = 0 Solution
(2) For which values of a and b does the following pair of linear equations have an infinite many solution
2x + 3y = 7
(a – b)x + (a + b)y = 3a + b – 2
(3) For which value of k will the following pair of linear equations have no solution
3x + y = 1
(2k – 1)x + (k – 1)y = 2k + 1 Solution
(4) Form the pair of linear equations in the following
problems and find their solutions (if they exist) by any algebraic method:
(i) A part of monthly hostel charges is fixed and remaining depends on the number of days one has taken food in the mess. When a student A takes food for 20 days she has to pay Rs.1000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs.1180 as hostel charges. Find the fixed charge and the cost of food per day. Solution
(ii) A fraction becomes 1/3 when 1 is subtracted from the numerator it becomes 1/4 when 8 is added to its denominator. Find the fraction. Solution
(iii) Yash scored 40 marks in a test, getting 3 marks for each right answer and losing 1 mark for each wrong answer. Had 4 marks been awarded for each correct answer and 2 marks been deducted for each incorrect answer, then Yash would have scored 50 marks. How many questions were there in the test? Solution
(iv) Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the car travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other ,they meet in 1 hour. What are the speeds of the two cars? Solution
(v) The area of a rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breadth increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 square units. Find the dimensions of the rectangle.
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