# SOLVING LINEAR EQUATIONS USING CROSS MULTIPLICATION METHOD WORKSHEET

(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

(iii) 3x – 5y  =  20 and 6x – 10y  =  40

(iv) x – 3y – 7  =  0 and 3x – 3y – 15  =  0

(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

(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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