1.
The cost of a computer is half the cost of a TV. Write a linear
equation in two variables to represent this statement.
2.
Which one of the following
options is true, for (a) & (b) and why?
(i) (0, 2) (ii)
(1 , - 1) (iii)
(4, 0)
3.
Find the value of m, if x =
3, y =
is a solution of the
equation 2x + 3y – m = 5
4.
Draw the graph of each of
the following linear equations in two variables: 3 = 2x + y
5.
Give the equations of two
lines passing through (2, - 7). How many more such lines are there, and why?
6.
If the point (3, 4) lies on
the graph of the equation 3y = ax + 7,
find the value of a.
7.
The taxi fare in a city is as follows: For the first 2
kilometers, the fare is Rs 8 and for the subsequent distance it is Rs 7 per km.
taking the distance covered as x km and total fare as Rs y, writes a linear
equation for this information, and draw its graph.
(b) If a passenger is to
travel from Railway station to Bus stand how much amount he will have to pay .
(what information is missing if not possible to calculate?
8. DELETED
9.
In countries like USA and
Canada, temperature is measured in Fahrenheit, whereas in countries like India,
it is measured in Celsius. Here is a linear equation that converts Fahrenheit
to Celsius:
F= 9C/5 + 32
(i) Draw the graph of the
linear equation above using Celsius for x-axis and Fahrenheit for y-axis.
(ii) If the temperature is
40°C, what is the temperature in Fahrenheit?
(iii) If the temperature is
35°F, what is the temperature in Celsius?
(iv) If the temperature is
0°C, what is the temperature in Fahrenheit and if the temperature is 0°F, what
is the temperature in Celsius?
(v) Is there a temperature
which is numerically the same in both Fahrenheit and Celsius? If yes, find it.
10. Write the equation
of x – axis and y – axis.
(a ) y = 3x + 5 (b) 3y + 7 = 0
(i) a unique solution, (ii) only two solutions, (iii)
infinitely many solutions
11. Write four solutions for each of the following equations:
(i) πx + y = 10 (ii)
x = 4y
12. Check which of the following are solutions of the equation x
– 3y = 4 and which are not:
13. In a two digit number, the unit's digit is twice the ten's
digit. If 27 is added to the number, the digits interchange their places. Find
the number. ( 36 )
14. In a two digit number, the ten's digit is three times the
unit's digit. When the number is decreased by 54, the digits are reversed. Find
the number. (96 )
15. A two digit number is such that the ten's digit exceeds twice the
unit's digit by 2 and the number obtained by inter-changing the digits is 5
more than three times the sum of the digits. Find the two digit number. (83)
16. If three times of my son's age is subtracted from my age, the
result is 10 years and if twice my age is added to my son's age, the result is 97 years. Find the
ages of both of us (43;11 yrs
)
17. The ages of A and B are in the ratio of 11 : 4. In 15 years,
their ages will be in the ratio of2:l Find their ages. (55
; 20 yrs )
18. Five times the age of a man is twelve times the age of his
son. 5 years ago, the ratio of their ages was
11: 4. Find their present ages. (60
&25 yrs )
19. The age of father is 3 years more than three times the age of
his son. Three years hence, father's age will be 10 years more than twice the age of the son.
Determine their present ages. (33 & 10 yrs ) The age of father is four times the sum of
ages of his two sons. Five years hence (later), father's age will be 1 year
more than twice the age of the son. Determine father’s present ages. (32) Find two numbers, which differ by
7, such that twice the greater added to five times the smaller makes 42. (11&4)
20. The sum of two numbers is 43. If twice the larger of these two
numbers exceeds three times the smaller by
36 ; find the numbers. (33&10 )
21. Sonali went to a bank to withdraw Rs 20000. She asked the
cashier to give her Rs 500 and Rs 1000 notes only. Sonali got 25 notes in all.
Find how many notes of Rs 500 and Rs
1000 she received. (10,15)
22. A man has certain notes of denominations Rs 20 and Rs 5
which amount to Rs 380. If the number of notes of each kind are interchanged,
they amount to Rs 60 less as before. Find the number of notes of each
denomination. (16,
20)
23. Express y in terms of x, given that 2x – 5y =7. Check
whether the point (–3,–2) is on the given line.
24. Express x in terms of y, given that 3x + 4y = 6. Check whether
the point (3, 2) is on given line.
25. Five years hence, father's age will be three times the age
of his son. Five years ago, father was seven times as old as his son-Find their present ages. (40; 10 yrs )
26. Express x in terms of y, it is being given that 7x – 3y =15.
Check if the line represented by the given equation intersects the y-axis at y
= –5.
27. Find the point of intersection of the line represented by
the equation 7x + y= –2 with y-axis. Check whether the point (2, 1) is a solution
of the given equation.
28. A part of monthly expenses of a family on milk is fixed
which is Rs.500 and the remaining varies with the quality of milk taken extra
the rate of Rs.20 per kg. Taking the quantity of milk required extra as x kg
and the total expenditure on milk Rs y. write a linear equation for this
information and draw its graph.
29. When 5 times the larger of the two numbers is divided by the
smaller, the quotient and remainder are 2 and 9 respectively. Form a linear
equation in two variables for above and give its two solutions.
Graphs
30. Draw the graph of 2x+y =7. Write the points where line meets
x and y–axis.
31. Draw the graph of the equation x –3y = 4. From the graph
find the value of x when y = –2.
32. Draw the graph of the equation 2x +5y =13. Find the points
where the line meets two axis.
33. Plot the graph of the following linear equation 2(x+3)
–3(y+1) =0. Also answer the following questions:
a) Write the quadrant in
which the line segment intercepted between the axes lie.
b) Shade the triangular
region formed by the line and the axes.
c) Write the vertices of
the triangle so formed.
34. “ Two years later
a father will be 8 years more than three times the age of the son” taking the
present age of father and son as x and y respectively . Write a linear equation
for above and draw its graph .From the graph, find the age of the father when
the son’s age is 10 years.
35. If the work done by a body on application of a constant force
is directly proportional to the distance travelled by the body. Express this in
the form of an equation in two variables and draw the graph of the same by
taking the constant force as 5 units .Also read from the graph the work done
when the distance travelled by the body is (a) 2 units (b) 0 unit.
36. Yamini and Fatima, two students of Class IX of a school,
together contributed Rs.100 towards the Prime Minister’s Relief Fund to the help
the earthquake victims. Write a linear equation which satisfies this data. (
You may take their contributions as Rs x and Rs. y ) Draw the graph of the
same.
37. Draw the graphs of the linear equations y = x and y = – x on
the same Cartesian plane .What do you observe.
38. Draw the graph of the equation represented by a straight
line which is parallel to the x–axis and at a distance 3 units below it
39. The sum of a two digit number and the number obtained by
reversing the order of digits is 121, and the two digits differ by 3. Find the
numbers (74,47)
40. The sum of the digits of a two digit number is 8 and the
difference between the number and that formed by reversing the digits is 18.
Find the number. (35;53)
41. Draw the graph of the linear equation whose solutions are
represented by the points having the sum of the coordinates as 10 units.
42. If “the cost of 5 tables exceed the cost of eight chairs by
Rs. 150”. Write the linear equation in two variables to represent the
statement. Also find the cost of one table if cost of one chair is Rs.240.
43. Draw the lines x =4, y=2 and x=y, on the same graph paper
and then identify what type of figure obtained? Also write the point of
vertices of this figure formed.
44. Ram is half of his father’s age .Twenty years ago the age of father
was six times age of Ram. Find the age of Ram and his father.
45. For the first kilometer, the fare is Rs. 5 and for
successive distance it is Rs2 per km. Taking distance covered as x and total fare
Rs. y. Write a linear equation and draw its graph.
46. The cost of a pen is 5 times the cost of a pencil. Write a
linear equation in two variables to represent the statement.
47. Find m, if point (7, –3) lies on the equation
48. Draw the graph of the linear equation y = mx + c, m=
and c =
Read from the graph, the value of x, when y =
4.5.
49. Water is flowing into a water tank at the same rate of 20 cubic
cm/sec. If the volume of water collected in x seconds is y cubic cm then write
a linear equation and
(a) Draw the graph of
linear equation.
(b) Find the volume of
water after 5 seconds.
50. Express the following linear equations in the form ax + by +
c = 0 and indicate the values of a, b and c in each case:
(i) x –
–
= 0 (ii) x = 3y (iii) y – 2 = 0 (iv) 5 = 2x
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