## Important questions of Maths class 10 chapter 3

## Important questions of Maths class 10 chapter 3

**CLASS- X**

**CH-3 PAIR OF LINEAR EQUATIONS IN TWO VARIABLE**

__OBJECTIVE TYPE QUESTIONS__

- For what value of k the lines 5x + 7y = 3 and 15x + 21y = k coincide?
- A pair of linear equations which have a unique solution x = 2, y = -3 is. (a) x + y = -1 ; 2x â€“ 3 y = -5 (b) 2x + 5 y = -11 ; 4x + 10 y = -22

(c ) 2x â€“ y = 1 ; 3x + 2y = 0 (d) x â€“ 4y â€“ 14 = 0 ; 5x â€“ y â€“ 13 = 0

- 3. How many solutions the pair of equations y = 0 and y = -7 has ?
- 4. Which types of lines, the pair of equation x = a and y = b represent?
- 5. Five years ago, A was thrice as old as B and ten years later, A shall be twice as old as B. What is the present age of A?

__SUBJECTIVE TYPE QUESTIONS__

6. If 217 x + 131 y = 913, 131 x + 217 y = 827 , then find x + y.

7. If bx â€“ ay = a + b and ax + by = a â€“ b, then find the value of x/y.

8. Find the value(s) of k for which the pair of linear equations 3x â€“ 2y â€“ 7 = 0 and 6x + ky +11 = 0 have a unique solution.

9. A fraction becomes if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator, it becomes Â½. Find the fraction?

10. The sum of a 2 digit number and the number obtained by reversing the digits is 66. If the digits of the numbers differ by 2; find the number. How many such numbers are their?

11. For what values of k will the following pair of linear equations given below has infinitely many solutions? Kx+3y-(k-3) =0

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â 12x+ky-k=0

12. The area of rectangle gets reduced by 9 sq. units, if its length is reduced by 5 units and breadth is increased by 3 units. If we increase length by 3 units and breadth by 2 units the area increases by 67 sq. units. Find the dimensions of the rectangle.

13. Solve the following pair of equations by reducing them to a pair of linear equations.

14. Solve the following equation-

px + qy = p-q ; qx â€“ py = p+q

15. 2 men and 7 boys can do a piece of work in 4 days. It is done by 4 men and 4 boys in 3 days. How long would it take for one man and one boy to do it?

Important questions of Maths class 10 chapter 3

16. The angles of a triangle are x, y and 40^{0}.The difference between the two angles x and y is 30^{0}. Find x and y.

17. Solve algebraically each of the following pair of linear equations for x and y

- 37 x + 43 y = 123

- 43 x + 37 y = 117

18 Solve the given system of equations by cross multiplication method

x + y = a + b

ax â€“ by = a^{2} â€“ b^{2}

19. X takes 3 hours more than y to walk 30 km. But if X doubles his pace, he is ahead of y by 1 hours. Find their speed of walking.

20. The sum of a two digit number and the number formed by interchanging the digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits of the first no. Find the first number.

21. The monthly income of A and B are in the ratio of 9 : 7. If their monthly expenditures are in the ratio 4 :3. If each saves Rs 1600 per month. Find the monthly incomes of each?

22. Fatherâ€™s age is 3 times the sum of ages of two children. After 5 years his age will be twice the sum of age of two children. Find the age of the father.

23. A sailor goes 8 km downstream in 40 minutes and return in 1 hour. Find the speed of the sailor in still water and the speed of the current.

24. Solve 2x + y = 6 and 2x â€“ y + 2 =0 graphically. Also find the area of the triangular region bounded by these lines and the x axis.

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## Important questions of Maths class 10 chapter 3

## Important questions of Maths class 10 chapter 3