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LINEAR EQUATIONS IN TWO VARIABLES
1. Point (3,4) lies on the graph of the equation 3y = kx + 7. The value of k is:
a. 4/3 b. 5/3. c.3 d. 7/3
2. The solution of equation x-2y = 4 is:
a. (0,2) b. (2,0) c.(4,0) d.(1,1)
3. The graph of Y = 6 is a line
a. Parallel to X axis at distance 6 units from the origin
b. Parallel to Y axis at a distance 6 units from the origin
c. Both A and B
d. None of the above
4. Is ax+by+c=0, where a,b&c are real numbers, is a linear equation in two variables?
a. Yes b. No c. Can’t say d. Not possible
5. The equation 2x+y=4 has a unique solution if x,y are
a. Rational numbers b. Real number c. natural numbers
d. Positive real numbers
6. The equation y=2x+3 has
a. A unique solution
b. No solution
c. Many solution
d. Two solutions
7. The number of lines passing through point (2,3) are
a. Only one b. Two c. many lines d. Two solutions
8. Which of the following are solution of the equation x+2y=7
a. (1,3) b. (3,1) c.(1,-3) d.(0,0)
9. Check which of the following are solutions of the equation x-2y=4 and which are not?
a. (0,2) b. (2,0) c. (4,0) d. (1,1)
10. The graph of the line x-y=0 passes through the point
a. b. c. d.
βˆ’
1
2
,
1
2
( )
3
2
, βˆ’
3
2
( )
0 , βˆ’ 1 ( ) 1 , 1 ( )
11. The linear equation 2x-5y=7 has
a. A unique solution
b. Two solution
c. Infinitely many solutions
d. No solution
12. If (3,1) is a solution of the linear equation 4x-5y=k, then the value of k is
a. 7 b. 13 c. 5 d. 12
13. x=5 and y=2 is a solution of the linear equation
a. x+2y = 7 b. x+y = 7 c. 5x+2y = 7 d. 5x+y = 7
14. Which of the linear equations satisfy the values of x= 1, y= 3.5?
a. x+y=7
b. x-2y=8
c. 2y-x=6
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d. y-x=3
15. Any point on line x=y is of the form :
a. (k,-k) b. (0,k) c. (k,0) d. (k,k)
16. The linear equation 3x-5y=15 has
a. Unique solution b. Two solutions c. many solution d. No solution
17.
18. Express the following linear equations in the form of ax +by +c = 0 and indicate the
values of a, b and c in each case:
a. -2x + 3y = 6
b. y - 2 = 0
19. If the point (2,5) lies on the graph of the equation 3y = ax + 7, find the value of a.
20. The taxi fare in a city is as follows : For the first kilometer, the fare is Rs. 8 and for the
subsequent distance it is Rs. 5 per km. Taking the distance covered as x km and total
fare as Rs y, write a linear equation for this information, and draw Its graph.
21.
𝐼𝑓 π‘₯ + 3 𝑦 = π‘˜ , 𝑓𝑖𝑛𝑑 π‘˜ 𝑖𝑓
3
5
,
1
6
( )
𝑖𝑠 π‘Ž π‘ π‘œπ‘™π‘’π‘‘π‘–π‘œπ‘› π‘œπ‘“ π‘‘β„Žπ‘’ 𝑔𝑖𝑣𝑒𝑛 π‘’π‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› .
22. Write equations of three lines passing through the point (2,1).
23. Express the linear equations in the form of ax+by+c=0 and indicate the values of a, b
and c
a. 3x=7y
b. -2x+3y=12
24. In which quadrant do the points (-3,5) and (4,-2) lie.
25. If x=-1 and y=2 is a solution of the equation 3x+4y=k. Find the value of k.
26. Write three solutions of the equation 3x+4y=7
27. and also find the
π‘Šπ‘Ÿπ‘–π‘‘π‘’ π‘‘β„Žπ‘’ π‘’π‘žπ‘’π‘Žπ‘‘π‘–π‘œπ‘› 4 π‘₯ = 6 ( 1 βˆ’ 𝑦 )+ 3 π‘₯ 𝑖𝑛 π‘‘β„Žπ‘’ π‘“π‘œπ‘Ÿπ‘š π‘œπ‘“ π‘Žπ‘₯ + 𝑏𝑦 = 𝑐
coordinates of the points where its graph cuts the two axes.
28. The taxi fare in a city is as follows: For the first kilometre, the fare is ` 8 and for the
subsequent distance it is ` 5 per km. Taking the distance covered as x km and total fare
as ` y, write a linear equation for this information, and find 3 solutions to the equation.
29. The cost of a notebook is 5 more than twice the cost of a pen. Write a linear equation in
two variables to represent this statement. Write two solutions of the equation.
30. Write four solutions for the equation: 2x+y=7
31. Express 7x-5=0 in the form of ax+by+c=0 and indicate the values of a, b and c.
32. If the point (5,9) lies on the graph of the equation 3y = ax+7, find the value of a.
33. Draw the graph of x+y=7
34. Write four solution for the equation:- 2x+y=7
35. If the point (3,4) lies on the graph of the equation 3y = ax +7, find the value of a.
36. FInd two solutions for given equation:- 3x+4y=12
37. Draw the graph for 2x+3y=6.
38. Rajat has to attend his sister’s marriage. He purchased 4 shirts and 2 trousers and paid
Rs. 2400. If cost of each shirt is Rs x and cost of each trouser is Rs y, answer the
following:-
a. Represent the above situation as a linear equation in two variables.
b. If the cost of one trouser is Rs. 700. Find the cost of one shirt.
c. Find the cost of 2 trousers if the cost of one shirt is Rs 300.
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d. Find the cost of 3 shirts if the cost of 2 trousers is Rs700.
39. Swastik is a bright student in his class and he is Selected to participate in the inter
School Quiz show in the show, the anchors give him a situation that 3 years ago the
mother's age was 20 years more than the Son's age. The Sum of the present age is 30
years, the anchor asks him to answer the following questions. based on the given
situations.
a. What could be the linear equation of the Sum of Present ages of the son and his
mother in variables x and y respectively?
a. What is the present age of the son?
b. What is the present age of the mother?
40. In countries like the 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 =
9
5
( )
𝐢 + 32
a. If the temperature is 30Β°C, what is the temperature in Fahrenheit?
b. If the temperature is 95Β°F, what is the temperature in Celsius?
c. If the temperature is 0Β°C, what is the temperature in Fahrenheit and if the
temperature is 0Β°F, what is the temperature in Celsius?
d. Is there a temperature which is numerically the same in both Fahrenheit and
Celsius? If yes, find it