CH-3 PAIR LINEAR EQUATIONS IN TWO VARIABLES CLASS-10
MCQS
Pair of linear Equations In Two Variables Class 10 Extra Questions
- For what value of k the lines 5x + 7y = 3 and 15x + 21y = k coincide?
a) 9Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â b. 12Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â c. 6Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â d. 28Â Â
2. Â How many solutions the pair of equations y = 0 and y = -7 has?
a) 1                        b. 2                         c. 0                     d. infinitely many            Â
3. At what point the pair of equations x = a and y = b intersect?
a) (0,0)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â b. (b, a)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â c. (a, b)Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â d. (1,1)
4. The pair of equations ax +2y = 9 and 3x +by =18 represent parallel lines, where a, b are integers ,if Â
a) a=b                    b. 3a=2b                 c. 2a=3b             d. ab=6  Â
5. If 2x +3y=15 and 3x+2y =25, then the value of x-y is :
a) -10Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â b. 8Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â c. 10Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â d. -8Â
SUBJECTIVE TYPE QUESTIONS
6. 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?
7. Solve :Â 2x +3y =17 and 2x+2 – 3y+ 1 =5 .
8. If  217 x + 131 y = 913   ; 131 x + 217 y = 827, then find x + y.
9. Find the area of the triangle bounded by line x/5 + y/7 =1 , x axis and y-axis ?
10. If bx – ay = a + b and ax + by = a – b, then find the value of x/y.
 11. A fraction becomes
9/11 , if 2 is added to both numerator and denominator. If 3 is added to both numerator and denominator, it becomes ½. Find the fraction.
 12. 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 there?
 13. For what values of k will the following pair of linear equations given below has infinitely many solutions?   Â
   Kx+3y-(k-3) =0 ,  12x+ky-k=0
 14. Find c if the system of equations cx + 3y + ( 3-c ) = 0; 12x + cy – c = 0 has infinitely many solutions?Â
15. 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.
16. Solve the given equation :      p x + q y = p-q ;    q x – p y = p + q
17. The angles of a triangle are x, y and 400.The difference between two angles x and y is 300,find x & y.
18. Solve the given system of equations by elimination method  : x + y = a + b ; ax – by = a2 – b2
19. 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.
20. 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?
21. In a den ,there are rabbits and hens. If they have 35 heads 98 feet, how many rabbits and hen are there ?
22. Father’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. Anuj had some chocolates and he divided them into two lots A and B . He sold the first lot at the rate of Rs. 2 for 3 chocolates and the 2nd lot at the rate of Re1 per chocolate and got a total of Rs 400. If he had sold the first lot at the rate of Re1 per chocolate and 2nd lot at the rate of Rs 4 for 5 chocolates, his total collection would have been Rs 460. Find the total number of chocolates he had .
25. Solve 2x + y = 6 and 2x – y + 2 =0 graphically. Also find the area of the triangular region bounded by these lines and the x axis.
26. Sumit is 3 times as old as his son. Five years later, he shall be two and a half times as old as his son. How old is Sumit at present?
27. A passenger train takes 2 hours less for a journey if its speed is increased by 5km/hr from its usual speed .It takes 30 minutes more if its speed is decreased by 1km/hr. Find the usual speed of the train ?
28. The sum of the numerator and denominator of a fraction is 4 more than twice the numerator. If the numerator and denominator each are increased by 3, they are in the ratio 2:3. Determine the fraction.
29. Half of the difference between 2 numbers is 2. The sum of the greater number and the twice the smaller number is 13. Find the numbers.
30. Find the value of k for which the pair of equations kx=y+2 and 6x=2y+3 has infinitely many solutions.
31. Find the area of the triangle formed by the line x/a + y/b =1 with the coordinate axis .
32. Two people are 16 km apart on a straight road. They start walking at the same time. If they walk towards each other with different speeds, they will meet in 2 hours. Had they walked in the same direction with same speed as before, they would have met in 8 hours. Find their walking speeds.
33. Find the area of the triangle formed by the lines x=3 , y=4 , and x= y .
34. If x=a and y=b is the solution of the pair of equations x-y=2 , x+y=4, find the values of a and b.
35. The sum of the ages of 2 children is a . The age of the father is twice the a . After 20 years , his age will be equal to the addition of the ages of his children. Find the age of the father.
36. Assertion (A):The solution of  pair of linear equations x + y = 5 & 2x – 3y = 4 is x = 19/5 & y = 6/5
Reason (R):The solution of pair of linear equations 3x + 4y = 10 and 2x – 2y = 2 is x = 2 and y = 1
37. Assertion (A): The value of q =
, if x = 3, y = 1 is the solution of the line 2x + y – q2 – 3 = 0.
Reason ( R ) : The solution of the line will satisfy the equation of the line.
Case Study Based Questions
Two schools P and Q decided to award prizes to their students for 2 games of Hockey Rs.x per student and Cricket Rs.y per student. School P decided to Award a total of Rs. 9500 for the two games to 5 and 4 Students respectively, while School Q decided to award Rs.7374 for the two games 4 and 3 students respectively.
(i) Represent the following information algebraically ( in terms of x and y).
(ii) What is the price amount of hockey?
(iii) On which game  the price amount is more and by how much ?
(iv) What will be the total Price amount if there are two student each part 2 games
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Pair of linear Equations In Two Variables Class 10 Extra Questions
Pair of linear Equations In Two Variables Class 10 Extra Questions
Pair of linear Equations In Two Variables Class 10 Extra Questions
Pair of linear Equations In Two Variables Class 10 Extra Questions
Pair of linear Equations In Two Variables Class 10 Extra Questions
Pair of linear Equations In Two Variables Class 10 Extra Questions
Pair of linear Equations In Two Variables Class 10 Extra Questions
