Linear Equations in Two Variables | Class 9 | Problem Set 5
Linear Equations in Two Variables | Class 9 | Problem Set 5, miscellaneous examples based on linear equations are solved in this article.
Problem-Set-5The examples of this problem set are dependent on the following topics –
(1) Finding solution of the given linear equations using elimination method.
(2) Finding solution of the linear equations using substitution method.
(3) Solving word problems on linear equations.
(4) Solving special types of linear equations.
Also read : Linear Equations in Two Variables | Class 9 | Practice Set 5.1
The examples of this problem set are given below –
(1) Choose the correct alternative answers for the following questions.
(i) If 3x + 5y = 9 and 5x + 3y = 7 then What is the value of x + y ?
(A) 2 (B) 16 (C) 9 (D) 7
(ii) When 5 is subtracted from length and breadth of the rectangle, the perimeter becomes 26.’ What is the mathematical form of the statement ?
(A) x – y = 8 (B) x + y = 8 (C) x + y = 23 (D) 2x + y = 21
(iii) Ajay is younger than Vijay by 5 years. Sum of their ages is 25 years. What is Ajay’s age ?
(A) 20 (B) 15 (C) 10 (D) 5
(2) Solve the following simultaneous equations.
(i) 2x + y = 5 ; 3x – y = 5 (iii) x + y = 11 ; 2x – 3y = 7 (ii) x – 2y = -1 ; (iv) 2x + y = -2 ; 2x- y = 7
(v) 2x – y = 5 ; 3x + 2y = 11 (vi) x – 2y = -2 ; x + 2y = 10
(3) By equating coefficients of variables, solve the following equations.
(i) 3x – 4y=7; 5x + 2y=3 (ii) 5x + 7y=17 ; 3x – 2y=4 (iii) x – 2y= -10; 3x – 5y= -12 (iv) 4x + y=34 ; x + 4y= 16
Class 9 | Problem Set 5 :
(4) Solve the following simultaneous equations.
(5) A two digit number is 3 more than 4 times the sum of its digits. If 18 is added to this number , the sum is equal to the number obtained by interchanging the digits. Find the number.
(6) The total cost of 8 books and 5 pens is 420 rupees and the total cost of 5 books and 8 pens is 321 rupees. Find the cost of 1 book and 2 pens.
(7) The ratio of incomes of two persons is 9 : 7. The ratio of their expenses is 4 : 3. Every person saves rupees 200, find the income of each.
(8) If the length of a rectangle is reduced by 5 units and its breadth is increased by 3 units, then the area of the rectangle is reduced by 8 square units. If length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 67 square units. Then find the length and breadth of the rectangle.
Also read : Linear Equations in Two Variables | Class 9 | Practice Set 5.2
(9) The distance between two places A and B on road is 70 kilo-meters. A car starts from A and the other from B. If they travel in the same direction, they will meet after 7 hours. If they travel towards each other they will meet after 1 hour, then find their speeds.
(10) The sum of a two digit number and the number obtained by interchanging its digits is 99. Find the number.
