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 the equation
    • (
      −
      4
      7
      x
      +
      9
      		)
      =
      0
  • (i)
    63
    4
  • (ii)
    31
    2
  • (iii)
    33
    2
  • (iv)
    65
    4
  • (v)
    61
    4
Question 2
2.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        6
        )
        ,
        (
        −
        2
        )
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        (
        −
        1
        )
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        0
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        1
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        2
        )
    • ?
  • (i)
    y
    =
    5
  • (ii)
    y
    =
    (
    −
    7
    6
    x
    −
    2
    		)
  • (iii)
    (
    −
    14
    x
    −
    12
    y
    +
    38
    		)
    =
    0
  • (iv)
    (
    8
    x
    +
    20
    y
    −
    5
    		)
    =
    0
  • (v)
    x
    =
    (
    −
    6
    		)
Question 3
3.
    • Solve
    • (
      2
      x
      −
      2
      y
      +
      1
      		)
      =
      0
      (
      −
      x
      −
      4
      y
      −
      4
      		)
      =
      0
  • (i)
    (
    (
    -4
    5
    		 )
    ,
    (
    -7
    8
    		 )
    )
  • (ii)
    (
    (
    -8
    7
    		 )
    ,
    (
    -7
    10
    		 )
    )
  • (iii)
    (
    (
    -6
    5
    		 )
    ,
    (
    -7
    10
    		 )
    )
  • (iv)
    (
    (
    -8
    7
    		 )
    ,
    (
    -7
    8
    		 )
    )
  • (v)
    (
    (
    -4
    5
    		 )
    ,
    (
    -9
    10
    		 )
    )
Question 4
4.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        2
        )
        ,
        197
        11
        )
      • ,
      • (
        (
        −
        1
        )
        ,
        185
        11
        )
      • ,
      • (
        0
        ,
        173
        11
        )
      • ,
      • (
        1
        ,
        161
        11
        )
      • ,
      • (
        2
        ,
        149
        11
        )
    • ?
  • (i)
    x
    =
    8
  • (ii)
    (
    −
    12
    x
    −
    11
    y
    +
    17
    		)
    =
    0
  • (iii)
    x
    =
    (
    12
    11
    y
    +
    4
    11
    		)
  • (iv)
    (
    2
    x
    +
    2
    y
    −
    1
    		)
    =
    0
  • (v)
    y
    =
    (
    −
    12
    11
    x
    +
    173
    11
    		)
Question 5
5.
    • Which of the following equations is not equivalent to
    • (
      −
      6
      x
      −
      3
      		)
      =
      1
  • (i)
    (
    −
    12
    x
    		)
    =
    8
  • (ii)
    12
    x
    =
    (
    −
    8
    		)
  • (iii)
    (
    −
    30
    x
    		)
    =
    20
  • (iv)
    (
    −
    6
    x
    		)
    =
    1
  • (v)
    30
    x
    =
    (
    −
    20
    		)
Question 6
6.
    • Which of the following equations is not the same as
    • (
      7
      x
      −
      5
      		)
      =
      (
      −
      2
      x
      +
      1
      		)
  • (i)
    (
    8
    x
    −
    1
    		)
    =
    (
    −
    x
    +
    5
    		)
  • (ii)
    (
    9
    x
    −
    8
    		)
    =
    (
    −
    2
    		)
  • (iii)
    (
    6
    x
    −
    9
    		)
    =
    (
    −
    3
    x
    −
    3
    		)
  • (iv)
    (
    5
    x
    −
    2
    		)
    =
    (
    −
    4
    x
    +
    4
    		)
  • (v)
    (
    8
    x
    −
    1
    		)
    =
    (
    −
    3
    x
    −
    3
    		)
Question 7
7.
A motor boat can move at a speed of 10.91 m/sec in still water. If it goes upstream for 460.46 sec, it travels a distance of 3412.00 m. What is the speed of the stream?
  • (i)
    2.50 m/sec
  • (ii)
    1.50 m/sec
  • (iii)
    4.50 m/sec
  • (iv)
    3.50 m/sec
  • (v)
    5.50 m/sec
Question 8
8.
    • Solve :
    •   −  
       
       
      3
       
       
      (
      x
      −
      3
      		)
      		  −  
       
       
      2
       
       
      (
      x
      +
      4
      		)
      =
        −  
       
       
      4
       
       
      (
      x
      +
      4
      		)
      		  −  
       
       
      1
       
       
      (
      x
      −
      2
      		)
  • (i)
    10
    7
  • (ii)
    2
  • (iii)
    8
    5
  • (iv)
    6
    5
Question 9
9.
    • Solve :
    •  
       
      (
      x
      −
      2
      		)
      		  +  
       
       
      (
      −
      x
      −
      5
      		)
      =
       
       
      (
      x
      −
      4
      		)
       
       
      4
  • (i)
    -25
  • (ii)
    -23
  • (iii)
    -26
  • (iv)
    -22
  • (v)
    -24
Question 10
10.
    • The point of intersection of x-axis and y-axis
  • (i)
    (
    1
    ,
    0
    )
  • (ii)
    (
    0
    ,
    2
    )
  • (iii)
    (
    1
    ,
    1
    )
  • (iv)
    (
    5
    ,
    0
    )
  • (v)
    (
    0
    ,
    0
    )
Question 11
11.
    • Solve :
    •   −  
       
       
      9
       
       
      (
      x
      +
      4
      		)
      		  +  
       
       
      4
       
       
      (
      x
      −
      1
      		)
      =
       
       
      1
       
       
      (
      x
      −
      1
      		)
      		  −  
       
       
      6
       
       
      (
      x
      −
      3
      		)
  • (i)
    27
    19
  • (ii)
    29
    19
  • (iii)
    31
    21
  • (iv)
    31
    19
  • (v)
    27
    17
Question 12
12.
    • Find the set of points satisfying the equation
    		•
      y
      =
      (
      −
      3
      x
      −
      14
      		)
  • (i)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      15
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      16
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      14
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      18
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      14
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      16
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      14
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      17
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
Question 13
13.
    • Solve
    • (
      4
      x
      +
      3
      y
      −
      1
      		)
      =
      (
      −
      2
      x
      +
      5
      y
      		)
      (
      x
      −
      5
      y
      +
      2
      		)
      =
      (
      −
      x
      +
      2
      y
      +
      3
      		)
  • (i)
    (
    7
    38
    ,
    (
    -2
    17
    		 )
    )
  • (ii)
    (
    5
    38
    ,
    (
    -2
    19
    		 )
    )
  • (iii)
    (
    7
    38
    ,
    (
    -4
    19
    		 )
    )
  • (iv)
    (
    1
    8
    ,
    (
    -2
    17
    		 )
    )
  • (v)
    (
    1
    8
    ,
    (
    -2
    19
    		 )
    )
Question 14
14.
    • Solve the equation
    • (
      −
      x
      −
      3
      		)
      =
      5
  • (i)
    -8
  • (ii)
    -5
  • (iii)
    -11
  • (iv)
    -9
  • (v)
    -7
Question 15
15.
A student walks from his house to school at 4.62 kmph and arrives 10.00 min late. The next day he walks at 16.33 kmph and reaches the school 32.90 min before time. At what speed must he travel to reach the school on time?
  • (i)
    4.54 kmph
  • (ii)
    3.54 kmph
  • (iii)
    5.54 kmph
  • (iv)
    6.54 kmph
  • (v)
    7.54 kmph
Question 16
16.
The ratio of two numbers is
4
:
2
and their LCM is 60. Find the numbers.
  • (i)
    60
    		:
    30
  • (ii)
    52
    		:
    26
  • (iii)
    64
    		:
    32
  • (iv)
    56
    		:
    28
  • (v)
    68
    		:
    34
Question 17
17.
    • Solve the equation
    • (
      x
      +
      9
      		)
      =
      0
  • (i)
    -8
  • (ii)
    -9
  • (iii)
    -11
  • (iv)
    -10
  • (v)
    -7
Question 18
18.
    • Which of the following equations is the same as
    • (
      −
      8
      x
      −
      7
      		)
      =
      (
      −
      3
      		)
  • (i)
    (
    −
    8
    x
    −
    14
    		)
    =
    (
    −
    6
    		)
  • (ii)
    (
    −
    8
    x
    −
    6
    		)
    =
    (
    −
    6
    		)
  • (iii)
    (
    −
    8
    x
    −
    10
    		)
    =
    (
    −
    6
    		)
  • (iv)
    (
    −
    8
    x
    −
    10
    		)
    =
    (
    −
    1
    		)
  • (v)
    (
    −
    8
    x
    −
    10
    		)
    =
    (
    −
    11
    		)
Question 19
19.
    • Which of the following equations is not equivalent to
    • (
      9
      x
      +
      2
      		)
      =
      (
      −
      3
      x
      +
      3
      		)
  • (i)
    12
    x
    =
    2
  • (ii)
    60
    x
    =
    5
  • (iii)
    (
    −
    48
    x
    		)
    =
    (
    −
    4
    		)
  • (iv)
    (
    −
    60
    x
    		)
    =
    (
    −
    5
    		)
  • (v)
    (
    −
    12
    x
    		)
    =
    (
    −
    1
    		)
Question 20
20.
    • Solve :
    •  
       
      (
      x
      +
      1
      		)
      		  +  
       
       
      (
      x
      −
      1
      		)
       
       
      5
      =
       
       
      (
      x
      −
      4
      		)
       
       
      2
  • (i)
    -5
  • (ii)
    -3
  • (iii)
    -2
  • (iv)
    -4
  • (v)
    -6
Question 21
21.
    • Due to a leak at the bottom, pipe Y takes
    • 8
      3
      4
      hr
    • to fill the tank.
    • The leak alone can empty the full tank in
    • 35
      hr
    • .
    • In what time can pipe Y alone fill the tank when the leak is closed?
  • (i)
    4
    hr
  • (ii)
    7
    hr
  • (iii)
    6
    hr
  • (iv)
    9
    hr
  • (v)
    8
    hr
Question 22
22.
    • Find the set of points satisfying the equation
    • (
      2
      x
      +
      7
      y
      −
      1
      		)
      =
      0
  • (i)
    • (
      (
      −
      2
      )
      ,
      5
      7
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      3
      7
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      13
      7
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      1
      7
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      3
      7
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      5
      7
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      3
      7
      )
    • ,
    • (
      0
      ,
      1
      7
      )
    • ,
    • (
      1
      ,
      (
      −
      1
      7
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      3
      7
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      5
      7
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      3
      7
      )
    • ,
    • (
      1
      ,
      (
      −
      6
      7
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      1
      7
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      3
      7
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      5
      7
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      3
      7
      )
    • ,
    • (
      0
      ,
      1
      7
      )
    • ,
    • (
      0
      ,
      6
      7
      )
    • ,
    • (
      2
      ,
      (
      −
      3
      7
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      5
      7
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      3
      7
      )
    • ,
    • (
      0
      ,
      1
      7
      )
    • ,
    • (
      1
      ,
      (
      −
      1
      7
      )
      )
    • ,
    • (
      4
      ,
      11
      7
      )
Question 23
23.
Two numbers are in the ratio 4 : 14. If 10 is added to each number, the ratio becomes 19 : 54. Find the numbers.
  • (i)
    32
    		:
    112
  • (ii)
    20
    		:
    70
  • (iii)
    24
    		:
    84
  • (iv)
    28
    		:
    98
  • (v)
    36
    		:
    126
Question 24
24.
    • Which of the following equations is equivalent to
    • (
      −
      9
      x
      −
      6
      		)
      =
      (
      −
      5
      x
      −
      4
      		)
  • (i)
    (
    −
    4
    x
    		)
    =
    (
    −
    1
    		)
  • (ii)
    (
    −
    4
    x
    		)
    =
    6
  • (iii)
    (
    −
    4
    x
    		)
    =
    2
  • (iv)
    (
    −
    4
    x
    		)
    =
    5
  • (v)
    (
    −
    4
    x
    		)
    =
    (
    −
    2
    		)
Question 25
25.
    • Which of the displayed lines represent the equation
    • y
      =
      (
      −
      5
      		)
  • (i)
      • line with point
      • P
  • (ii)
      • line with point
      • R
  • (iii)
      • line with point
      • Q
  • (iv)
      • line with point
      • T
  • (v)
      • line with point
      • S
    Assignment Key
  •  1) (i)
  •  2) (v)
  •  3) (iii)
  •  4) (v)
  •  5) (iv)
  •  6) (v)
  •  7) (iv)
  •  8) (iii)
  •  9) (v)
  •  10) (v)
  •  11) (ii)
  •  12) (v)
  •  13) (ii)
  •  14) (i)
  •  15) (iii)
  •  16) (i)
  •  17) (ii)
  •  18) (iii)
  •  19) (i)
  •  20) (iv)
  •  21) (ii)
  •  22) (ii)
  •  23) (iv)
  •  24) (iii)
  •  25) (i)