Q.1. Draw the graph of
2y = 4x – 6 2x = y+ 3
And determine whether this system of linear equation has a unique solution of not.
Q.2. solve the following system of linear equation:
5x – 6y + 30 = 0 5x + 4y – 20 =0
Find the vertices of the triangle formed by the above two lines and x-axis.
Q.3. solve graphically the system of linear equation:
4x – 3y + 4 = 0 4x + 3y – 20 = 0
Find the area of the region bounded by these lines and x-axis.
Q.4. find value of k for which the systems of equation have a unique solution:
X – ky = 2 3x + 2y = -5
Q.5. find value of k for which the systems of equation has no solution:
3x – y – 5 =0 6x – 2y – k = 0
Q.6. determine the value of c for which the following system of linear equation has no solution.
Cx + 3y = 3 12x + cy = 6
Q.7.for what value of k, the following system of equation have (1) a unique solution (2) no solution
2x + ky =1 3x-5y = 7
Q.8. for what value of k, the following system of equation have (1) a unique solution (2) no solution
4x –y = 11 kx + 3y = 5
Q.9. for what value of k, the following pair of linear equation has infinitely many solutions?
Kx + 5y – (k – 5) = 0
Q.10. for what value of k, will the following system of equation have infinite solution?
2x – 3y = 7, (k + 2)x –(2k + 1)y = 3(3k – 1)
Q.11. find the value of for which the following system of linear equations has infinite solutions:
X + (α + 1) y = 4 (α + 1)x + 9y = 5α + 2
Q.12. for what values of a and b does the following system of linear equation have an infinite number of solution?
2x + 3y = 7, a(x+y) – b(x –y) = 3a + b – 2
Q.13. find the value of k for which k for which the following system of linear has infinite solution:
X + (k + 1) y = 5, (k + 1) x + 9y = 8k – 1
Q.15. 5 books and 7 pens together cost Rs. 79 whereas 7 books and 5 pens together cost Rs. 77. Find the total cost of 1 book and 2 pens. (Ans. Rs.20 )
Q.16. the sum of the numerator and the denominator of a fraction is 12. If the denominator increased by 3, the fraction become ½. Find the fraction. (Ans. 5/7)
Q.17. two year ago, a father was five times as old as his son. Two year later, his age will be 8 more than three times the age of the son. Find the present ages of father and son (Ans. 42, 10
Q.18. the sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number. (Ans.57)
Q.19.a boat goes 12 km upstream and 40 km downstream in 8 hours. It can go 16 km upstream and 32 km downstream in the same time. Find the speed of the boat in still water and the speed of the stream. (Ans. 6km/hr, 2km/hr.)
Q.20. the area of a rectangle gets reduced by 80 sq. units if its length is reduced by 5 units and the breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area is increased by 50 sq. units. Find the length and breadth of the rectangle. (Ans.40, 30)
Q.21. a man has only 20 paisa coins and 25 paisa coins in his purse. If he has 50 coins in all totaling Rs. 11.25, how many coins of each does he have? (Ans.25)
Q.22. Taxi charges consist of fixed charges and the remaining depending upon the distance travelled in kilometers. If a person travels 10 km, he pays Rs 68 and for travelling 15 km, he pays Rs. 98. (Ans. 3, 3.5 per/km)
Q.23. Abdul travelled 300 km by train and 200 km by taxi. It took him 5 hours 30 minutes. But if he travels 260 km train and 240 km by taxi, he takes 6 minutes longer. Find the speed of the train and that of the taxi. (Ans. Train-1000km/hr. taxi- 80 km/hr. )
Q.1. aftab tells his daughter, seven years ago, I was seven times as old as you were then. Also, three years from now, I shall be three times as ols as you will be, represent this situation algebraically and graphically.
Q.2. The coach of a cricket team buys 3 bats and 6 balls of for Rs. 3,900. Later she buys another bat and 3 more balls of the same kind for Rs. 1,300. Represent this situation algebraically and geometrically.
Q.3. the cost of 2 kg of apples and 1 kg of grapes on a day was found to be Rs. 160. After a month, the cost of 4 kg of apples and 2 kg of graphs is Rs. 300. Represent the situation algebraically and geometrically.
Q.4. form the pair of linear equation in the following problems, and find their solutions graphically.
a. 10 student of class 10th took p0art in a mathematics quiz. If the number of girls is 4 more than the number of boys, find the number of boys and girls who took part in the quiz.
b. 5 pencils and 7 pens together cost Rs. 50, whereas 7 pencils and 5 pens together cost Rs. 46. Find the cost of one pencil and that of one pen.
c. half the perimeter of a rectangular garden, whose length is 4 m more than its with, is 36 m. find the dimensions of garden.
Q.5. Draw the graphs of the equations x-y + 1 =0 and 3x + 2y- 12 = 0. Determine the coordinates of the vertices of the triangle formed by these lines and the x-axis, and shade the triangular region.
Q.6. form the pair of linear equations for the following problems and find their solution by substitution method.
a. the difference between two numbers is 26 one number is three times the other. Find them.
b. the larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
C. the coach of a cricket team buys 7 bats and 6 balls for Rs. 3800. Later, she buys 3 bats and 5 balls for Rs. 1750. Find the cost of each bat and each ball.
D. the taxi charges in a city consists of a fixed charge together with the charge for the distance of 10 km, the charge paid is Rs. 105. And for a journey of 15 km, the charge paid is Rs. 155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
E. a fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If 3 is added to both the numerator and the denominator, it becomes 5/6. Find the fraction.
F. five year hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Q.7. solve pair of linear equations by elimination method.
A. if we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes ½ if we only add 1 to the denominator. What is the fraction?
B. five years ago, Nuri was thrice as old as sonu. Ten years later, Nuri will be twice as old as sonu. How old are Nuri and sonu?
C. the sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.
d. Meena went to a bank to withdraw Rs. 2,000. She asked the cashier to gives her Rs. 50. And Rs. 100. Notes only. Meena got 25 notes in all. Find how many notes of Rs.50. and Rs. 100 she received
E. a lending library has a fixed charge for first three days and an addition charge for each day thereafter. Saritha paid Rs. 27. For a book kept for seven days, while susy paid Rs. 21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Q. the pair of linear equations for the following problems and find their solution by suitable method.
I. a part of monthly hostel charges is fixed and the 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. 1, 0000 as hostel charges whereas a student B, who takes food for 26 days, pays Rs. 1180 as hostel charges. Find the fixed charges and the cost of food per day.
ii. A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes ¼ when 8 is added to its denominator. Find the fraction.
iii. Yash scored 40 marks is 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?
iv. Place A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If they travel toward each other, they meet in 1 hour. What is the speed of the two cars?
V. the area of rectangle gets reduced by 9 square units, if its length is reduced by 5 units and breath is increeced 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.
vi. Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of speed of rowing in still water and the speed of the current.
vii. 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, also that taken by 1 man alone.
viii. Roohi travels 300 km to her home party by train and party by bus. She taken 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer find the speed of the train and the bus separately.
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