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 following pair of equations :
    •  
       
      x
      		  +  
       
       
      14
       
       
      y
      =
       
       
      64
    •  
       
      5
      x
      		  +  
       
       
      4
       
       
      y
      =
       
       
      56
  • (i)
    (
    8
    ,
    1
    4
    )
  • (ii)
    (
    8
    ,
    1
    2
    )
  • (iii)
    (
    8
    ,
    (
    -1
    4
    		 )
    )
  • (iv)
    (
    9
    ,
    1
    4
    )
  • (v)
    (
    10
    ,
    1
    4
    )
Question 2
2.
The ratio of males to females in a committee of 126 members is 4 : 5. How many more ladies should be added to the committee so that the ratio of males to females is 7 : 15?
  • (i)
    52
  • (ii)
    50
  • (iii)
    51
  • (iv)
    47
  • (v)
    49
Question 3
3.
Find the equation of the displayed line
  • (i)
    3
    y
    =
    7
  • (ii)
    y
    =
    8
  • (iii)
    y
    =
    6
  • (iv)
    y
    =
    7
  • (v)
    x
    =
    7
Question 4
4.
    • Which of the following equations is the same as
    • (
      x
      −
      7
      		)
      =
      (
      6
      x
      +
      3
      		)
  • (i)
    (
    2
    x
    −
    4
    		)
    =
    5
    x
  • (ii)
    (
    −
    2
    x
    −
    5
    		)
    =
    (
    9
    x
    +
    1
    		)
  • (iii)
    (
    4
    x
    −
    9
    		)
    =
    (
    9
    x
    +
    1
    		)
  • (iv)
    (
    −
    10
    		)
    =
    (
    7
    x
    +
    6
    		)
  • (v)
    (
    4
    x
    −
    9
    		)
    =
    (
    3
    x
    +
    5
    		)
Question 5
5.
    • Find the number which bears the same ratio
    • to
    • 2
      9
    • that
    • 3
      5
    • does to
    • 4
      15
  • (i)
    9
    16
  • (ii)
    1
    2
  • (iii)
    11
    18
  • (iv)
    7
    18
  • (v)
    9
    20
Question 6
6.
Which of the following is a linear equation in one variable?
  • (i)
    (
    −
    6
    x
    +
    6
    y
    −
    z
    +
    6
    		)
    =
    0
  • (ii)
    (
    −
    6
    x
    −
    3
    		)
    =
    0
  • (iii)
    (
    20
    x
    2
     
    −
    56
    x
    +
    32
    		)
    =
    0
  • (iv)
    (
    −
    5
    x
    +
    8
    y
    		)
    =
    0
  • (v)
    (
    8
    x
    2
     
    +
    17
    x
    y
    −
    78
    x
    +
    2
    y
    2
     
    −
    21
    y
    +
    54
    		)
    =
    0
Question 7
7.
    • Solve :
    •  
       
      (
      x
      −
      4
      		)
      		  +  
       
       
      (
      −
      x
      +
      3
      		)
       
       
      2
      =
       
       
      (
      −
      x
      −
      5
      		)
  • (i)
    -3
  • (ii)
    (
    -7
    3
    		 )
  • (iii)
    (
    -7
    5
    		 )
  • (iv)
    -1
  • (v)
    (
    -5
    3
    		 )
Question 8
8.
    • In a mixture of
    • 486
    • litres,
    • the ratio of milk and water is
    • 20 : 7
    • .
    • How much water must be added
    • to this mixture to make the ratio
    • 30 : 13
    • ?
  • (i)
    27
  • (ii)
    31
  • (iii)
    29
  • (iv)
    30
  • (v)
    33
Question 9
9.
    • Solve
    • (
      4
      x
      −
      y
      −
      1
      		)
      =
      0
      (
      5
      x
      +
      5
      y
      −
      3
      		)
      =
      0
  • (i)
    (
    8
    27
    ,
    7
    23
    )
  • (ii)
    (
    2
    5
    ,
    7
    23
    )
  • (iii)
    (
    8
    25
    ,
    7
    25
    )
  • (iv)
    (
    2
    5
    ,
    1
    5
    )
  • (v)
    (
    8
    27
    ,
    7
    25
    )
Question 10
10.
    • Solve the equation
    • (
      6
      x
      −
      9
      		)
      =
      (
      x
      −
      3
      		)
  • (i)
    6
    5
  • (ii)
    4
    5
  • (iii)
    8
    7
  • (iv)
    4
    3
  • (v)
    8
    5
Question 11
11.
    • Which of the following equations is not the same as
    • (
      −
      2
      x
      +
      7
      		)
      =
      0
  • (i)
    (
    2
    x
    −
    7
    		)
    =
    0
  • (ii)
    (
    4
    x
    −
    14
    		)
    =
    0
  • (iii)
    (
    8
    x
    −
    28
    		)
    =
    (
    −
    4
    		)
  • (iv)
    (
    −
    6
    x
    +
    21
    		)
    =
    0
  • (v)
    (
    −
    4
    x
    +
    14
    		)
    =
    0
Question 12
12.
    • Solve the equation
    • (
      −
      9
      2
      x
      +
      5
      2
      		)
      =
      (
      4
      3
      x
      −
      5
      3
      		)
  • (i)
    3
    7
  • (ii)
    1
  • (iii)
    5
    9
  • (iv)
    5
    7
Question 13
13.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        2
        )
        ,
        0
        )
      • ,
      • (
        (
        −
        1
        )
        ,
        0
        )
      • ,
      • (
        0
        ,
        0
        )
      • ,
      • (
        1
        ,
        0
        )
      • ,
      • (
        2
        ,
        0
        )
    • ?
  • (i)
    (
    −
    13
    x
    −
    5
    y
    +
    4
    		)
    =
    0
  • (ii)
    y
    =
    0
  • (iii)
    y
    =
    (
    −
    13
    5
    x
    −
    52
    5
    		)
  • (iv)
    (
    4
    x
    +
    9
    y
    −
    3
    		)
    =
    0
  • (v)
    x
    =
    (
    13
    5
    y
    −
    4
    		)
Question 14
14.
Find the equation of the displayed line
  • (i)
    x
    =
    7
  • (ii)
    x
    =
    6
  • (iii)
    y
    =
    6
  • (iv)
    x
    =
    5
  • (v)
    3
    x
    =
    6
Question 15
15.
    • Solve :
    •  
       
      1
       
       
      (
      x
      −
      3
      		)
      		  −  
       
       
      2
       
       
      (
      x
      −
      6
      		)
      =
       
       
      3
       
       
      (
      x
      −
      6
      		)
      		  −  
       
       
      4
       
       
      (
      x
      −
      9
      		)
  • (i)
    0
  • (ii)
    2
  • (iii)
    3
  • (iv)
    1
  • (v)
    -1
Question 16
16.
    • Solve the following pair of equations :
    •  
       
      1
       
       
      √
      x
      		  +  
       
       
      9
       
       
      √
      y
      =
      25
    •  
       
      4
       
       
      √
      x
      		  +  
       
       
      6
       
       
      √
      y
      =
      40
  • (i)
    (
    3
    49
    ,
    1
    4
    )
  • (ii)
    (
    1
    49
    ,
    1
    2
    )
  • (iii)
    (
    1
    51
    ,
    1
    4
    )
  • (iv)
    (
    1
    49
    ,
    (
    -1
    4
    		 )
    )
  • (v)
    (
    1
    49
    ,
    1
    4
    )
Question 17
17.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        6
        )
        ,
        (
        −
        2
        )
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        (
        −
        1
        )
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        0
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        1
        )
      • ,
      • (
        (
        −
        6
        )
        ,
        2
        )
    • ?
  • (i)
    (
    −
    5
    x
    −
    8
    y
    +
    12
    		)
    =
    0
  • (ii)
    x
    =
    (
    −
    6
    		)
  • (iii)
    y
    =
    9
  • (iv)
    y
    =
    (
    −
    5
    8
    x
    +
    21
    4
    		)
  • (v)
    (
    7
    x
    +
    10
    y
    −
    5
    		)
    =
    0
Question 18
18.
    • Which of the displayed lines represent the equation
    • x
      =
      (
      −
      3
      		)
  • (i)
      • line with point
      • S
  • (ii)
      • line with point
      • W
  • (iii)
      • line with point
      • V
  • (iv)
      • line with point
      • T
  • (v)
      • line with point
      • U
Question 19
19.
    • Which of the following equations is the same as
    • (
      x
      −
      1
      		)
      =
      (
      −
      5
      		)
  • (i)
    (
    x
    −
    6
    		)
    =
    (
    −
    6
    		)
  • (ii)
    (
    x
    −
    2
    		)
    =
    (
    −
    1
    		)
  • (iii)
    (
    x
    +
    2
    		)
    =
    (
    −
    6
    		)
  • (iv)
    (
    x
    −
    2
    		)
    =
    (
    −
    11
    		)
  • (v)
    (
    x
    −
    2
    		)
    =
    (
    −
    6
    		)
Question 20
20.
A train crosses a telegraph post in 23.82 sec and a bridge 616.70 m long in 63.84 sec. What is the speed of the train?
  • (i)
    17.41 m/sec
  • (ii)
    14.41 m/sec
  • (iii)
    15.41 m/sec
  • (iv)
    13.41 m/sec
  • (v)
    16.41 m/sec
Question 21
21.
    • Which of the following equations is the same as
    • (
      −
      8
      x
      −
      4
      		)
      =
      1
  • (i)
    (
    −
    15
    x
    		)
    =
    (
    7
    x
    −
    3
    		)
  • (ii)
    (
    −
    15
    x
    −
    7
    		)
    =
    (
    7
    x
    +
    4
    		)
  • (iii)
    (
    −
    x
    −
    1
    		)
    =
    (
    −
    7
    x
    −
    2
    		)
  • (iv)
    (
    −
    x
    −
    8
    		)
    =
    (
    −
    7
    x
    +
    5
    		)
  • (v)
    (
    −
    15
    x
    		)
    =
    (
    −
    7
    x
    +
    5
    		)
Question 22
22.
    • Solve
    • (
      3
      x
      +
      3
      y
      +
      4
      		)
      =
      (
      −
      2
      		)
      (
      −
      4
      x
      −
      5
      y
      −
      1
      		)
      =
      (
      −
      4
      		)
  • (i)
    (
    -12
    ,
    10
    )
  • (ii)
    (
    -13
    ,
    11
    )
  • (iii)
    (
    -12
    ,
    11
    )
  • (iv)
    (
    -11
    ,
    10
    )
  • (v)
    (
    -11
    ,
    8
    )
Question 23
23.
    • Find the set of points satisfying the equation
    • (
      −
      3
      x
      +
      y
      −
      11
      		)
      =
      0
  • (i)
    • (
      (
      −
      2
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      8
      )
    • ,
    • (
      0
      ,
      11
      )
    • ,
    • (
      0
      ,
      15
      )
    • ,
    • (
      2
      ,
      17
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      8
      )
    • ,
    • (
      1
      ,
      10
      )
    • ,
    • (
      1
      ,
      14
      )
    • ,
    • (
      2
      ,
      17
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      8
      )
    • ,
    • (
      0
      ,
      11
      )
    • ,
    • (
      1
      ,
      14
      )
    • ,
    • (
      4
      ,
      19
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      8
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      9
      )
    • ,
    • (
      1
      ,
      14
      )
    • ,
    • (
      2
      ,
      17
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      5
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      8
      )
    • ,
    • (
      0
      ,
      11
      )
    • ,
    • (
      1
      ,
      14
      )
    • ,
    • (
      2
      ,
      17
      )
Question 24
24.
    • Which of the following equations is not the same as
    • (
      −
      2
      x
      −
      9
      		)
      =
      (
      −
      6
      		)
  • (i)
    (
    −
    2
    x
    −
    6
    		)
    =
    (
    −
    3
    		)
  • (ii)
    (
    −
    2
    x
    −
    4
    		)
    =
    (
    −
    1
    		)
  • (iii)
    (
    −
    2
    x
    −
    5
    		)
    =
    (
    −
    10
    		)
  • (iv)
    (
    −
    2
    x
    −
    14
    		)
    =
    (
    −
    11
    		)
  • (v)
    (
    −
    2
    x
    −
    12
    		)
    =
    (
    −
    9
    		)
Question 25
25.
Two numbers are in the ratio 8 : 19. If 20 is added to each number, the ratio becomes 10 : 21. Find the numbers.
  • (i)
    80
    		:
    190
  • (ii)
    72
    		:
    171
  • (iii)
    64
    		:
    152
  • (iv)
    88
    		:
    209
  • (v)
    96
    		:
    228
    Assignment Key
  •  1) (i)
  •  2) (ii)
  •  3) (iv)
  •  4) (iii)
  •  5) (ii)
  •  6) (ii)
  •  7) (v)
  •  8) (iv)
  •  9) (iii)
  •  10) (i)
  •  11) (iii)
  •  12) (iv)
  •  13) (ii)
  •  14) (ii)
  •  15) (iv)
  •  16) (v)
  •  17) (ii)
  •  18) (i)
  •  19) (v)
  •  20) (iii)
  •  21) (v)
  •  22) (ii)
  •  23) (v)
  •  24) (iii)
  •  25) (i)