EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Equations and Simultaneous Linear Equations
Grade : ICSE Grade IX
License : Non Commercial Use
Question 1
1.
A motor boat can travel at a speed of 25.28 m/sec downstream and 5.96 m/sec upstream. How much distance can the boat travel in 26.82 sec in still water?
  • (i)
    418.93 m
  • (ii)
    420.93 m
  • (iii)
    416.93 m
  • (iv)
    417.93 m
  • (v)
    419.93 m
Question 2
2.
    • Which of the following equations is the same as
    • (
      −
      6
      x
      −
      6
      		)
      =
      (
      2
      x
      −
      5
      		)
  • (i)
    (
    2
    x
    −
    11
    		)
    =
    (
    −
    6
    x
    		)
  • (ii)
    (
    −
    14
    x
    −
    1
    		)
    =
    (
    10
    x
    −
    10
    		)
  • (iii)
    (
    2
    x
    −
    9
    		)
    =
    (
    −
    6
    x
    −
    2
    		)
  • (iv)
    (
    −
    14
    x
    −
    1
    		)
    =
    (
    −
    6
    x
    		)
  • (v)
    (
    −
    14
    x
    −
    3
    		)
    =
    (
    10
    x
    −
    8
    		)
Question 3
3.
A train crosses a telegraph post in 31.32 sec and a bridge 1422.91 m long in 72.95 sec. What is the speed of the train?
  • (i)
    32.18 m/sec
  • (ii)
    36.18 m/sec
  • (iii)
    34.18 m/sec
  • (iv)
    33.18 m/sec
  • (v)
    35.18 m/sec
Question 4
4.
    • Which of the following equations is the same as
    • (
      −
      2
      x
      −
      2
      		)
      =
      0
  • (i)
    (
    −
    4
    x
    −
    9
    		)
    =
    0
  • (ii)
    (
    −
    4
    x
    −
    4
    		)
    =
    0
  • (iii)
    (
    −
    4
    x
    −
    4
    		)
    =
    (
    −
    4
    		)
  • (iv)
    (
    −
    4
    x
    −
    4
    		)
    =
    4
  • (v)
    (
    −
    4
    x
    +
    1
    		)
    =
    0
Question 5
5.
    • Solve :
    •  
       
      (
      −
      x
      −
      5
      		)
      		  +  
       
       
      (
      x
      −
      4
      		)
       
       
      2
      =
       
       
      (
      −
      x
      		)
  • (i)
    11
  • (ii)
    17
  • (iii)
    13
  • (iv)
    15
  • (v)
    14
Question 6
6.
    • Solve the equation
    • (
      7
      x
      −
      2
      		)
      =
      0
  • (i)
    0
  • (ii)
    2
    9
  • (iii)
    4
    7
  • (iv)
    2
    5
  • (v)
    2
    7
Question 7
7.
    • Which of the following equations is the same as
    • (
      −
      7
      x
      −
      6
      		)
      =
      0
  • (i)
    (
    −
    9
    x
    −
    5
    		)
    =
    (
    −
    2
    x
    +
    1
    		)
  • (ii)
    (
    −
    12
    x
    −
    8
    		)
    =
    (
    5
    x
    +
    2
    		)
  • (iii)
    (
    −
    9
    x
    −
    5
    		)
    =
    (
    2
    x
    −
    1
    		)
  • (iv)
    (
    −
    2
    x
    −
    4
    		)
    =
    (
    −
    5
    x
    −
    2
    		)
  • (v)
    (
    −
    5
    x
    −
    7
    		)
    =
    (
    −
    2
    x
    +
    1
    		)
Question 8
8.
    • Solve
    •  
    • (
      3
      x
      +
      5
      y
      +
      13
      		)
      =
      0
      (
      2
      x
      −
      3
      y
      +
      15
      		)
      =
      0
  • (i)
    (
    (
    −
    6
    )
    ,
    1
    )
  • (ii)
    (
    (
    −
    4
    )
    ,
    3
    )
  • (iii)
    (
    8
    ,
    9
    )
  • (iv)
    (
    (
    −
    8
    )
    ,
    (
    −
    1
    )
    )
  • (v)
    (
    4
    ,
    8
    )
Question 9
9.
    • The value of
    • x
    • in terms of other variables and constant in
    • (
      4
      x
      −
      2
      y
      −
      9
      		)
      =
      (
      −
      x
      +
      8
      y
      −
      3
      		)
    • is
  • (i)
    x
    =
    (
    y
    +
    6
    5
    		)
  • (ii)
    x
    =
    (
    2
    y
    +
    4
    5
    		)
  • (iii)
    x
    =
    (
    3
    y
    +
    6
    5
    		)
  • (iv)
    x
    =
    (
    2
    y
    +
    6
    5
    		)
  • (v)
    x
    =
    (
    2
    y
    +
    8
    5
    		)
Question 10
10.
    • Which of the following equations is not the same as
    • (
      −
      6
      x
      −
      2
      		)
      =
      (
      −
      x
      −
      7
      		)
  • (i)
    (
    −
    6
    x
    −
    7
    		)
    =
    (
    −
    x
    −
    12
    		)
  • (ii)
    (
    −
    6
    x
    −
    5
    		)
    =
    (
    −
    x
    −
    10
    		)
  • (iii)
    (
    −
    6
    x
    +
    1
    		)
    =
    (
    −
    x
    −
    4
    		)
  • (iv)
    (
    −
    6
    x
    −
    3
    		)
    =
    (
    −
    x
    −
    6
    		)
  • (v)
    (
    −
    6
    x
    +
    3
    		)
    =
    (
    −
    x
    −
    2
    		)
Question 11
11.
    • The point of intersection of x-axis and y-axis
  • (i)
    (
    1
    ,
    1
    )
  • (ii)
    (
    0
    ,
    7
    )
  • (iii)
    (
    2
    ,
    0
    )
  • (iv)
    (
    0
    ,
    0
    )
  • (v)
    (
    1
    ,
    0
    )
Question 12
12.
    • Which of the displayed lines represent the equation
    • y
      =
      1
      2
      x
  • (i)
      • line with point
      • W
  • (ii)
      • line with point
      • X
  • (iii)
      • line with point
      • V
  • (iv)
      • line with point
      • U
  • (v)
      • line with point
      • T
Question 13
13.
The ratio of two numbers is
5
:
3
and their LCM is 150. Find the numbers.
  • (i)
    50
    		:
    30
  • (ii)
    45
    		:
    27
  • (iii)
    40
    		:
    24
  • (iv)
    55
    		:
    33
  • (v)
    60
    		:
    36
Question 14
14.
    • Find the set of points satisfying the equation
    		•
      y
      =
      (
      −
      11
      6
      x
      		)
  • (i)
    • (
      (
      −
      2
      )
      ,
      11
      3
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      11
      6
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      11
      6
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      11
      3
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      11
      3
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      11
      6
      )
    • ,
    • (
      0
      ,
      0
      )
    • ,
    • (
      1
      ,
      (
      −
      11
      6
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      5
      3
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      11
      3
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      11
      6
      )
    • ,
    • (
      0
      ,
      0
      )
    • ,
    • (
      1
      ,
      (
      −
      11
      6
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      11
      3
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      11
      3
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      11
      6
      )
    • ,
    • (
      0
      ,
      0
      )
    • ,
    • (
      0
      ,
      (
      −
      5
      6
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      11
      3
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      11
      3
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      11
      6
      )
    • ,
    • (
      1
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      11
      6
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      11
      3
      )
      )
Question 15
15.
    • Solve the following pair of equations :
    •   −  
       
       
      3
      x
      		  +  
       
       
      6
       
       
      y
      =
       
       
      (
      −
      33
      		)
    •  
       
      11
      x
      		  +  
       
       
      8
       
       
      y
      =
       
       
      (
      −
      29
      		)
  • (i)
    (
    1
    ,
    (
    -1
    7
    		 )
    )
  • (ii)
    (
    3
    ,
    (
    -1
    5
    		 )
    )
  • (iii)
    (
    2
    ,
    (
    -1
    5
    		 )
    )
  • (iv)
    (
    1
    ,
    1
    5
    )
  • (v)
    (
    1
    ,
    (
    -1
    5
    		 )
    )
Question 16
16.
Which of the following is a linear equation in three variable?
  • (i)
    (
    −
    5
    x
    −
    9
    y
    −
    4
    		)
    =
    0
  • (ii)
    (
    −
    3
    x
    −
    9
    		)
    =
    0
  • (iii)
    (
    −
    7
    x
    +
    3
    y
    +
    4
    z
    +
    2
    		)
    =
    0
  • (iv)
    (
    32
    x
    2
     
    +
    4
    x
    −
    45
    		)
    =
    0
  • (v)
    (
    −
    3
    x
    2
     
    −
    35
    x
    y
    +
    6
    x
    −
    72
    y
    2
     
    +
    35
    y
    −
    3
    		)
    =
    0
Question 17
17.
    • Solve
    •  
    • (
      8
      x
      +
      11
      y
      −
      1
      		)
      =
      0
      (
      8
      x
      +
      11
      y
      +
      52
      		)
      =
      0
  • (i)
    No solution
  • (ii)
    (
    (
    −
    1
    )
    ,
    (
    −
    4
    )
    )
  • (iii)
    (
    5
    ,
    (
    −
    7
    )
    )
  • (iv)
    (
    7
    ,
    (
    −
    5
    )
    )
  • (v)
    Infinite solutions
Question 18
18.
A line which is neither parallel to x-axis nor y-axis is
  • (i)
    an oblique line
  • (ii)
    a horizontal line
  • (iii)
    a curved line
  • (iv)
    a vertical line
Question 19
19.
    • Solve the equation
    • (
      x
      +
      3
      		)
      =
      0
  • (i)
    0
  • (ii)
    -3
  • (iii)
    -2
  • (iv)
    -4
  • (v)
    -5
Question 20
20.
    • Which of the following equations is the same as
    • (
      2
      x
      −
      7
      		)
      =
      (
      3
      x
      −
      9
      		)
  • (i)
    (
    −
    3
    x
    −
    15
    		)
    =
    (
    8
    x
    −
    1
    		)
  • (ii)
    (
    7
    x
    +
    1
    		)
    =
    (
    −
    2
    x
    −
    17
    		)
  • (iii)
    (
    x
    −
    6
    		)
    =
    (
    4
    x
    −
    10
    		)
  • (iv)
    (
    3
    x
    −
    8
    		)
    =
    (
    2
    x
    −
    8
    		)
  • (v)
    (
    −
    3
    x
    −
    15
    		)
    =
    (
    −
    2
    x
    −
    17
    		)
Question 21
21.
The speed of a motor boat is 18.99 m/sec and the speed of a stream is 6.60 m/sec. A & B are two location adjacent to a stream. If it takes 393.50 sec to go from point A to B and come back, What is the distance between A and B?
  • (i)
    3286.97 m
  • (ii)
    3284.97 m
  • (iii)
    3282.97 m
  • (iv)
    3283.97 m
  • (v)
    3285.97 m
Question 22
22.
    • Which of the following equations is the same as
    • (
      −
      5
      x
      +
      9
      		)
      =
      (
      −
      6
      x
      +
      7
      		)
  • (i)
    (
    −
    5
    x
    +
    14
    		)
    =
    (
    −
    6
    x
    +
    12
    		)
  • (ii)
    (
    −
    5
    x
    +
    10
    		)
    =
    (
    −
    6
    x
    +
    12
    		)
  • (iii)
    (
    −
    5
    x
    +
    18
    		)
    =
    (
    −
    6
    x
    +
    12
    		)
  • (iv)
    (
    −
    5
    x
    +
    14
    		)
    =
    (
    −
    6
    x
    +
    14
    		)
  • (v)
    (
    −
    5
    x
    +
    14
    		)
    =
    (
    −
    6
    x
    +
    10
    		)
Question 23
23.
    • Find the set of points satisfying the equation
    		•
      y
      =
      (
      2
      x
      −
      4
      		)
  • (i)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      2
      ,
      0
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      2
      ,
      0
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      2
      ,
      0
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      4
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      4
      ,
      2
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      6
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      5
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      2
      ,
      0
      )
Question 24
24.
    • Which of the following equations is the same as
    • (
      5
      x
      +
      9
      		)
      =
      0
  • (i)
    (
    −
    4
    x
    +
    17
    		)
    =
    (
    9
    x
    −
    8
    		)
  • (ii)
    (
    12
    x
    +
    18
    		)
    =
    (
    7
    x
    +
    9
    		)
  • (iii)
    (
    −
    2
    x
    		)
    =
    (
    7
    x
    +
    9
    		)
  • (iv)
    (
    14
    x
    +
    1
    		)
    =
    (
    −
    9
    x
    +
    8
    		)
  • (v)
    (
    12
    x
    +
    18
    		)
    =
    (
    −
    7
    x
    −
    9
    		)
Question 25
25.
A motor boat can move at a speed of 17.03 m/sec in still water. If it goes downstream for 169.45 sec, it travels a distance of 3911.00 m. What is the speed of the stream?
  • (i)
    4.05 m/sec
  • (ii)
    8.05 m/sec
  • (iii)
    5.05 m/sec
  • (iv)
    7.05 m/sec
  • (v)
    6.05 m/sec
    Assignment Key
  •  1) (i)
  •  2) (iv)
  •  3) (iii)
  •  4) (ii)
  •  5) (v)
  •  6) (v)
  •  7) (i)
  •  8) (i)
  •  9) (iv)
  •  10) (iv)
  •  11) (iv)
  •  12) (v)
  •  13) (i)
  •  14) (iii)
  •  15) (v)
  •  16) (iii)
  •  17) (i)
  •  18) (i)
  •  19) (ii)
  •  20) (v)
  •  21) (ii)
  •  22) (i)
  •  23) (ii)
  •  24) (ii)
  •  25) (v)