EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Equations and Simultaneous Linear Equations
Grade : ICSE Grade IX
License : Non Commercial Use
Question 1
1.
    • Solve :
    •  
       
      (
      −
      3
      x
      +
      4
      		)
       
       
      (
      −
      6
      x
      −
      8
      		)
      =
       
       
      (
      −
      3
      x
      −
      7
      		)
       
       
      (
      −
      6
      x
      +
      3
      		)
  • (i)
    (
    -2
    3
    		 )
  • (ii)
    (
    -4
    11
    		 )
  • (iii)
    (
    -4
    7
    		 )
  • (iv)
    (
    -4
    9
    		 )
  • (v)
    (
    -2
    9
    		 )
Question 2
2.
    • Which of the following equations is not the same as
    • (
      −
      7
      x
      −
      1
      		)
      =
      0
  • (i)
    (
    −
    7
    x
    +
    3
    		)
    =
    4
  • (ii)
    (
    −
    7
    x
    +
    4
    		)
    =
    (
    −
    5
    		)
  • (iii)
    (
    −
    7
    x
    −
    3
    		)
    =
    (
    −
    2
    		)
  • (iv)
    (
    −
    7
    x
    −
    5
    		)
    =
    (
    −
    4
    		)
  • (v)
    (
    −
    7
    x
    +
    1
    		)
    =
    2
Question 3
3.
A motor boat can travel at a speed of 29.24 m/sec downstream and 8.86 m/sec upstream. What is the speed of the motor boat in still water?
  • (i)
    20.05 m/sec
  • (ii)
    19.05 m/sec
  • (iii)
    18.05 m/sec
  • (iv)
    21.05 m/sec
  • (v)
    17.05 m/sec
Question 4
4.
    • Which of the following equations is not the same as
    • (
      6
      x
      +
      7
      		)
      =
      0
  • (i)
    (
    6
    x
    +
    8
    		)
    =
    1
  • (ii)
    (
    6
    x
    +
    4
    		)
    =
    3
  • (iii)
    (
    6
    x
    +
    3
    		)
    =
    (
    −
    4
    		)
  • (iv)
    (
    6
    x
    +
    6
    		)
    =
    (
    −
    1
    		)
  • (v)
    (
    6
    x
    +
    11
    		)
    =
    4
Question 5
5.
    • Solve
    •  
    • (
      −
      3
      x
      +
      10
      y
      +
      2
      		)
      =
      0
      (
      x
      −
      11
      y
      −
      16
      		)
      =
      0
  • (i)
    (
    (
    −
    5
    )
    ,
    (
    −
    3
    )
    )
  • (ii)
    (
    (
    −
    8
    )
    ,
    (
    −
    4
    )
    )
  • (iii)
    (
    (
    −
    6
    )
    ,
    (
    −
    2
    )
    )
  • (iv)
    (
    (
    −
    4
    )
    ,
    0
    )
  • (v)
    (
    (
    −
    7
    )
    ,
    (
    −
    1
    )
    )
Question 6
6.
    • The point of intersection of x-axis and y-axis
  • (i)
    (
    1
    ,
    0
    )
  • (ii)
    (
    0
    ,
    1
    )
  • (iii)
    (
    0
    ,
    0
    )
  • (iv)
    (
    1
    ,
    1
    )
Question 7
7.
A train crosses a telegraph post in 13.16 sec and a bridge 991.03 m long in 51.00 sec. What is the length of the train?
  • (i)
    342.66 m
  • (ii)
    343.66 m
  • (iii)
    345.66 m
  • (iv)
    346.66 m
  • (v)
    344.66 m
Question 8
8.
    • The L.H.S of the equation
    • (
      −
      x
      +
      9
      		)
      =
      (
      2
      x
      +
      9
      		)
    • is
  • (i)
    (
    −
    x
    +
    9
    		)
  • (ii)
    (
    −
    2
    x
    +
    9
    		)
  • (iii)
    (
    −
    x
    +
    12
    		)
  • (iv)
    (
    −
    x
    +
    6
    		)
  • (v)
    (
    2
    x
    +
    9
    		)
Question 9
9.
    • The additive inverse of the expression
    • (
      2
      x
      −
      1
      		)
    • is
  • (i)
    (
    −
    2
    x
    −
    2
    		)
  • (ii)
    (
    −
    2
    x
    +
    1
    		)
  • (iii)
    (
    2
    x
    −
    1
    		)
  • (iv)
    (
    −
    3
    x
    +
    1
    		)
  • (v)
    (
    −
    2
    x
    +
    3
    		)
Question 10
10.
    • Solve
    •  
    • (
      −
      11
      x
      −
      4
      y
      +
      9
      		)
      =
      0
      (
      y
      −
      5
      		)
      =
      0
  • (i)
    (
    (
    −
    1
    )
    ,
    0
    )
  • (ii)
    (
    3
    ,
    (
    −
    6
    )
    )
  • (iii)
    (
    0
    ,
    5
    )
  • (iv)
    (
    (
    −
    1
    )
    ,
    5
    )
  • (v)
    (
    (
    −
    6
    )
    ,
    (
    −
    7
    )
    )
Question 11
11.
    • Solve :
    •  
       
      (
      x
      +
      4
      		)
      		  +  
       
       
      (
      −
      x
      +
      4
      		)
       
       
      6
      =
       
       
      (
      −
      x
      +
      2
      		)
  • (i)
    (
    -16
    11
    		 )
  • (ii)
    (
    -14
    9
    		 )
  • (iii)
    (
    -18
    13
    		 )
  • (iv)
    (
    -18
    11
    		 )
  • (v)
    (
    -14
    11
    		 )
Question 12
12.
    • Solve :
    •  
       
      (
      −
      1
      		)
       
       
      (
      −
      7
      x
      +
      9
      		)
      =
       
       
      1
       
       
      (
      −
      7
      x
      +
      6
      		)
  • (i)
    17
    16
  • (ii)
    13
    12
  • (iii)
    13
    14
  • (iv)
    17
    14
  • (v)
    15
    14
Question 13
13.
    • Which of the following lines pass through the origin?
  • (i)
    (
    −
    9
    y
    −
    54
    		)
    =
    0
  • (ii)
    (
    4
    x
    −
    3
    y
    		)
    =
    0
  • (iii)
    (
    10
    x
    +
    2
    y
    −
    38
    		)
    =
    0
  • (iv)
    (
    4
    x
    +
    10
    y
    −
    52
    		)
    =
    0
  • (v)
    (
    −
    14
    x
    −
    3
    y
    −
    74
    		)
    =
    0
Question 14
14.
    • Which of the following equations is not the same as
    • (
      4
      x
      +
      1
      		)
      =
      (
      7
      x
      +
      9
      		)
  • (i)
    (
    4
    x
    +
    2
    		)
    =
    (
    7
    x
    +
    10
    		)
  • (ii)
    (
    4
    x
    +
    4
    		)
    =
    (
    7
    x
    +
    12
    		)
  • (iii)
    (
    4
    x
    −
    2
    		)
    =
    (
    7
    x
    +
    6
    		)
  • (iv)
    4
    x
    =
    (
    7
    x
    +
    8
    		)
  • (v)
    (
    4
    x
    +
    6
    		)
    =
    (
    7
    x
    +
    4
    		)
Question 15
15.
    • Find the set of points satisfying the equation
    		•
      x
      =
      (
      −
      1
      2
      y
      −
      15
      2
      		)
  • (i)
    • (
      (
      −
      2
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      13
      )
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      19
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      13
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      16
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      19
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      13
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      15
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      19
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      13
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      15
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      16
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      19
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      13
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      15
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      17
      )
      )
Question 16
16.
    • Solve the following pair of equations :
    •   −  
       
       
      14
       
       
      x
      		  −  
       
       
      2
       
       
      y
      =
       
       
      (
      −
      4
      		)
    •   −  
       
       
      3
       
       
      x
      		  +  
       
       
      7
       
       
      y
      =
       
       
      66
  • (i)
    (
    1
    -1
    ,
    1
    7
    )
  • (ii)
    (
    0
    ,
    1
    9
    )
  • (iii)
    (
    1
    -1
    ,
    (
    -1
    9
    		 )
    )
  • (iv)
    (
    1
    ,
    1
    9
    )
  • (v)
    (
    1
    -1
    ,
    1
    9
    )
Question 17
17.
The speed of a motor boat is 22.43 m/sec and the speed of a stream is 11.61 m/sec. A & B are two location adjacent to a stream. If it takes 253.95 sec to go from point A to B and come back, What is the distance between A and B?
  • (i)
    2083.00 m
  • (ii)
    2087.00 m
  • (iii)
    2086.00 m
  • (iv)
    2085.00 m
  • (v)
    2084.00 m
Question 18
18.
    • Solve the following pair of equations :
    •  
       
      10
      x
      		  −  
       
       
      9
       
       
      y
      =
       
       
      11
    •  
       
      5
      x
      		  +  
       
       
      1
       
       
      y
      =
       
       
      (
      −
      44
      		)
  • (i)
    (
    -7
    ,
    1
    9
    )
  • (ii)
    (
    -7
    ,
    (
    -1
    9
    		 )
    )
  • (iii)
    (
    -6
    ,
    (
    -1
    9
    		 )
    )
  • (iv)
    (
    -7
    ,
    (
    -1
    11
    		 )
    )
  • (v)
    (
    -5
    ,
    (
    -1
    9
    		 )
    )
Question 19
19.
    • Find the equation of the line passing through the points
    • (
      (
      −
      1
      )
      ,
      4
      )
    • and
    • (
      (
      −
      1
      )
      ,
      5
      )
  • (i)
    (
    x
    +
    1
    		)
    =
    0
  • (ii)
    x
    =
    0
  • (iii)
    (
    2
    x
    +
    1
    		)
    =
    0
  • (iv)
    1
    =
    0
Question 20
20.
    • Solve :
    •  
       
      (
      x
      +
      5
      		)
      		  +  
       
       
      (
      x
      +
      4
      		)
       
       
      14
      =
       
       
      (
      x
      +
      1
      		)
       
       
      7
  • (i)
    (
    -74
    13
    		 )
  • (ii)
    (
    -72
    13
    		 )
  • (iii)
    (
    -70
    13
    		 )
  • (iv)
    (
    -82
    15
    		 )
  • (v)
    (
    -62
    11
    		 )
Question 21
21.
    • Which of the following equations is not the same as
    • (
      2
      x
      +
      2
      		)
      =
      0
  • (i)
    (
    −
    4
    x
    −
    4
    		)
    =
    0
  • (ii)
    (
    8
    x
    +
    8
    		)
    =
    0
  • (iii)
    (
    6
    x
    +
    6
    		)
    =
    3
  • (iv)
    (
    −
    10
    x
    −
    10
    		)
    =
    0
  • (v)
    (
    4
    x
    +
    4
    		)
    =
    0
Question 22
22.
    • The linear equation
    • 6
      x
      =
      (
      9
      x
      −
      8
      		)
    • is equivalent to
  • (i)
    (
    −
    4
    x
    +
    8
    		)
    =
    0
  • (ii)
    6
    x
    =
    (
    9
    x
    −
    5
    		)
  • (iii)
    (
    −
    2
    x
    +
    8
    		)
    =
    0
  • (iv)
    (
    −
    3
    x
    +
    8
    		)
    =
    0
  • (v)
    6
    x
    =
    (
    9
    x
    −
    11
    		)
Question 23
23.
    • Which of the displayed lines represent the equation
    • y
      =
      8
  • (i)
      • line with point
      • W
  • (ii)
      • line with point
      • U
  • (iii)
      • line with point
      • V
  • (iv)
      • line with point
      • S
  • (v)
      • line with point
      • T
Question 24
24.
    • Which of the following equations is the same as
    • (
      7
      x
      +
      5
      		)
      =
      (
      8
      x
      +
      4
      		)
  • (i)
    (
    4
    x
    +
    6
    		)
    =
    (
    11
    x
    +
    3
    		)
  • (ii)
    (
    6
    x
    −
    3
    		)
    =
    (
    9
    x
    +
    12
    		)
  • (iii)
    (
    8
    x
    +
    13
    		)
    =
    (
    9
    x
    +
    12
    		)
  • (iv)
    (
    8
    x
    +
    13
    		)
    =
    (
    7
    x
    −
    4
    		)
  • (v)
    (
    10
    x
    +
    4
    		)
    =
    (
    5
    x
    +
    5
    		)
Question 25
25.
    • Which of the following equations is the same as
    • (
      3
      x
      +
      3
      		)
      =
      (
      −
      8
      		)
  • (i)
    (
    3
    x
    +
    7
    		)
    =
    (
    −
    7
    		)
  • (ii)
    (
    3
    x
    +
    4
    		)
    =
    (
    −
    12
    		)
  • (iii)
    (
    3
    x
    +
    4
    		)
    =
    (
    −
    7
    		)
  • (iv)
    (
    3
    x
    +
    4
    		)
    =
    (
    −
    2
    		)
  • (v)
    (
    3
    x
    +
    1
    		)
    =
    (
    −
    7
    		)
    Assignment Key
  •  1) (iv)
  •  2) (ii)
  •  3) (ii)
  •  4) (ii)
  •  5) (iii)
  •  6) (iii)
  •  7) (v)
  •  8) (i)
  •  9) (ii)
  •  10) (iv)
  •  11) (i)
  •  12) (v)
  •  13) (ii)
  •  14) (v)
  •  15) (iii)
  •  16) (v)
  •  17) (iv)
  •  18) (ii)
  •  19) (i)
  •  20) (ii)
  •  21) (iii)
  •  22) (iv)
  •  23) (iv)
  •  24) (iii)
  •  25) (iii)