EduSahara™ Worksheet
Name : Chapter Based Worksheet
Chapter : Linear Equations and Simultaneous Linear Equations
Grade : ICSE Grade IX
License : Non Commercial Use
Question 1
1.
Which of the following is a linear equation in two variable?
  • (i)
    (
    −
    5
    x
    +
    7
    		)
    =
    0
  • (ii)
    (
    −
    42
    x
    2
     
    +
    104
    x
    y
    +
    44
    x
    −
    64
    y
    2
     
    −
    48
    y
    +
    16
    		)
    =
    0
  • (iii)
    (
    8
    x
    2
     
    −
    4
    x
    −
    40
    		)
    =
    0
  • (iv)
    (
    −
    9
    x
    −
    3
    y
    +
    8
    		)
    =
    0
  • (v)
    (
    6
    x
    −
    9
    y
    −
    z
    +
    7
    		)
    =
    0
Question 2
2.
    • Which of the following equations is the same as
    • (
      −
      3
      x
      +
      5
      		)
      =
      0
  • (i)
    (
    −
    4
    x
    +
    5
    		)
    =
    x
  • (ii)
    (
    −
    4
    x
    +
    5
    		)
    =
    (
    −
    x
    		)
  • (iii)
    (
    −
    5
    x
    +
    10
    		)
    =
    (
    2
    x
    −
    5
    		)
  • (iv)
    (
    −
    x
    		)
    =
    (
    −
    2
    x
    +
    5
    		)
  • (v)
    (
    −
    2
    x
    +
    5
    		)
    =
    (
    −
    x
    		)
Question 3
3.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        2
        )
        ,
        5
        3
        )
      • ,
      • (
        (
        −
        1
        )
        ,
        1
        1
        )
      • ,
      • (
        0
        ,
        1
        3
        )
      • ,
      • (
        1
        ,
        (
        −
        1
        3
        )
        )
      • ,
      • (
        2
        ,
        (
        −
        1
        )
        )
    • ?
  • (i)
    y
    =
    (
    −
    13
    9
    x
    +
    13
    3
    		)
  • (ii)
    x
    =
    (
    13
    9
    y
    +
    3
    		)
  • (iii)
    y
    =
    0
  • (iv)
    x
    =
    3
  • (v)
    (
    2
    x
    +
    3
    y
    −
    1
    		)
    =
    0
Question 4
4.
    • Which of the following equations is not equivalent to
    • (
      −
      9
      x
      −
      3
      		)
      =
      (
      −
      2
      		)
  • (i)
    18
    x
    =
    (
    −
    2
    		)
  • (ii)
    (
    −
    9
    x
    		)
    =
    0
  • (iii)
    (
    −
    18
    x
    		)
    =
    2
  • (iv)
    27
    x
    =
    (
    −
    3
    		)
  • (v)
    (
    −
    9
    x
    		)
    =
    1
Question 5
5.
    • Which of the following equations is equivalent to
    • (
      9
      x
      +
      8
      		)
      =
      0
  • (i)
    9
    x
    =
    (
    −
    8
    		)
  • (ii)
    9
    x
    =
    (
    −
    7
    		)
  • (iii)
    9
    x
    =
    (
    −
    6
    		)
  • (iv)
    9
    x
    =
    (
    −
    9
    		)
  • (v)
    9
    x
    =
    (
    −
    10
    		)
Question 6
6.
Which of the following is a linear equation in one variable?
  • (i)
    (
    −
    4
    x
    +
    y
    +
    5
    		)
    =
    (
    7
    x
    +
    9
    y
    −
    5
    		)
  • (ii)
    (
    9
    x
    −
    y
    −
    z
    −
    5
    		)
    =
    (
    −
    7
    x
    +
    3
    y
    +
    5
    z
    +
    9
    		)
  • (iii)
    (
    8
    x
    2
     
    −
    46
    x
    y
    −
    12
    x
    −
    12
    y
    2
     
    +
    22
    y
    +
    4
    		)
    =
    0
  • (iv)
    (
    x
    +
    1
    		)
    =
    (
    6
    x
    −
    4
    		)
  • (v)
    (
    36
    x
    2
     
    +
    5
    x
    −
    24
    		)
    =
    (
    −
    9
    x
    +
    7
    		)
Question 7
7.
    • Find the set of points satisfying the equation
    		•
      y
      =
      (
      4
      x
      −
      28
      		)
  • (i)
    • (
      (
      −
      2
      )
      ,
      (
      −
      36
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      32
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      29
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      24
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      36
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      32
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      28
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      24
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      18
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      36
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      32
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      28
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      24
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      (
      −
      36
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      32
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      28
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      23
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      (
      −
      36
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      32
      )
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      30
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      24
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      20
      )
      )
Question 8
8.
    • Solve the following pair of equations :
    • (
      −
      4
      x
      +
      y
      		)
      =
      0
    • (
      −
      3
      x
      +
      8
      y
      		)
      =
      (
      −
      29
      x
      y
      		)
  • (i)
    (
    (
    -1
    4
    		 )
    ,
    -2
    )
  • (ii)
    (
    (
    -1
    2
    		 )
    ,
    1
    -1
    )
  • (iii)
    (
    (
    -1
    4
    		 )
    ,
    -4
    )
  • (iv)
    (
    (
    -1
    4
    		 )
    ,
    1
    -1
    )
  • (v)
    (
    (
    -3
    4
    		 )
    ,
    1
    -1
    )
Question 9
9.
    • The L.H.S of the equation
    • (
      2
      x
      +
      9
      		)
      =
      (
      −
      x
      +
      8
      		)
    • is
  • (i)
    (
    2
    x
    +
    12
    		)
  • (ii)
    (
    −
    x
    +
    8
    		)
  • (iii)
    (
    2
    x
    +
    6
    		)
  • (iv)
    (
    x
    +
    9
    		)
  • (v)
    (
    2
    x
    +
    9
    		)
Question 10
10.
    • The L.H.S of the equation
    • (
      −
      x
      +
      7
      		)
      =
      0
    • is
  • (i)
    0
  • (ii)
    (
    −
    x
    +
    10
    		)
  • (iii)
    (
    −
    x
    +
    5
    		)
  • (iv)
    (
    −
    x
    +
    7
    		)
  • (v)
    (
    −
    2
    x
    +
    7
    		)
Question 11
11.
    • 20
    • men and
    • 9
    • women can do a piece of work in
    • 5
    • days.
    • 3
    • men and
    • 2
    • women can do the same work in
    • 25
    • days.
    • In how many days can
    • 3
    • men and
    • 5
    • women complete the same work?
  • (i)
    11
    17
    30
    days
  • (ii)
    11
    15
    28
    days
  • (iii)
    11
    17
    26
    days
  • (iv)
    11
    19
    28
    days
  • (v)
    11
    17
    28
    days
Question 12
12.
    • Solve :
    •  
       
      (
      −
      9
      x
      −
      6
      		)
       
       
      (
      −
      8
      x
      +
      9
      		)
      =
       
       
      (
      −
      9
      		)
       
       
      5
  • (i)
    17
    37
  • (ii)
    17
    41
  • (iii)
    17
    39
  • (iv)
    5
    13
  • (v)
    19
    39
Question 13
13.
    • Solve the equation
    • (
      −
      2
      x
      		)
      =
      (
      −
      9
      		)
  • (i)
    11
    2
  • (ii)
    5
  • (iii)
    9
    2
  • (iv)
    7
    2
  • (v)
    17
    4
Question 14
14.
    • Find the number which bears the same ratio
    • to
    • 4
      8
    • that
    • 4
      5
    • does to
    • 16
      35
  • (i)
    7
    10
  • (ii)
    5
    8
  • (iii)
    7
    8
  • (iv)
    7
    6
  • (v)
    9
    8
Question 15
15.
    • Solve :
    •  
       
      3
       
       
      (
      x
      −
      3
      		)
      		  −  
       
       
      4
       
       
      (
      x
      +
      5
      		)
      =
        −  
       
       
      5
       
       
      (
      x
      +
      5
      		)
      		  +  
       
       
      4
       
       
      (
      x
      −
      2
      		)
  • (i)
    7
  • (ii)
    12
  • (iii)
    10
  • (iv)
    8
  • (v)
    9
Question 16
16.
    • Which of the following equations satisfy the given points
      • (
        (
        −
        5
        )
        ,
        (
        −
        2
        )
        )
      • ,
      • (
        (
        −
        5
        )
        ,
        (
        −
        1
        )
        )
      • ,
      • (
        (
        −
        5
        )
        ,
        0
        )
      • ,
      • (
        (
        −
        5
        )
        ,
        1
        )
      • ,
      • (
        (
        −
        5
        )
        ,
        2
        )
    • ?
  • (i)
    (
    −
    13
    x
    −
    15
    y
    +
    42
    		)
    =
    0
  • (ii)
    x
    =
    (
    13
    15
    y
    −
    51
    5
    		)
  • (iii)
    y
    =
    6
  • (iv)
    y
    =
    (
    −
    13
    15
    x
    +
    5
    3
    		)
  • (v)
    x
    =
    (
    −
    5
    		)
Question 17
17.
    • Solve the equation
    • (
      9
      2
      x
      −
      7
      3
      		)
      =
      8
      5
  • (i)
    118
    137
  • (ii)
    8
    9
  • (iii)
    118
    133
  • (iv)
    118
    135
  • (v)
    116
    135
Question 18
18.
A student walks from his house to school at 3.69 kmph and arrives 17.90 min late. The next day he walks at 9.60 kmph and reaches the school 5.30 min before time. At what speed must he travel to reach the school on time?
  • (i)
    5.03 kmph
  • (ii)
    8.03 kmph
  • (iii)
    6.03 kmph
  • (iv)
    9.03 kmph
  • (v)
    7.03 kmph
Question 19
19.
    • Which of the following equations is not the same as
    • (
      −
      5
      x
      −
      6
      		)
      =
      0
  • (i)
    (
    −
    8
    x
    −
    8
    		)
    =
    (
    −
    3
    x
    −
    2
    		)
  • (ii)
    (
    −
    6
    x
    −
    5
    		)
    =
    (
    −
    x
    +
    1
    		)
  • (iii)
    (
    −
    2
    x
    −
    4
    		)
    =
    (
    −
    3
    x
    −
    2
    		)
  • (iv)
    (
    −
    4
    x
    −
    7
    		)
    =
    (
    x
    −
    1
    		)
  • (v)
    (
    −
    2
    x
    −
    4
    		)
    =
    (
    3
    x
    +
    2
    		)
Question 20
20.
    • Solve
    •  
    • (
      4
      x
      +
      3
      y
      +
      14
      		)
      =
      0
      (
      −
      2
      x
      +
      y
      −
      12
      		)
      =
      0
  • (i)
    (
    (
    −
    5
    )
    ,
    2
    )
  • (ii)
    (
    (
    −
    6
    )
    ,
    3
    )
  • (iii)
    (
    (
    −
    3
    )
    ,
    4
    )
  • (iv)
    (
    (
    −
    7
    )
    ,
    0
    )
  • (v)
    (
    (
    −
    4
    )
    ,
    1
    )
Question 21
21.
Which of the following is a linear equation in three variable?
  • (i)
    (
    −
    7
    x
    −
    9
    		)
    =
    0
  • (ii)
    (
    7
    x
    −
    4
    y
    +
    8
    		)
    =
    0
  • (iii)
    (
    5
    x
    2
     
    +
    27
    x
    y
    +
    26
    x
    −
    56
    y
    2
     
    −
    33
    y
    +
    5
    		)
    =
    0
  • (iv)
    (
    −
    6
    x
    −
    9
    y
    +
    6
    z
    +
    7
    		)
    =
    0
  • (v)
    (
    48
    x
    2
     
    +
    72
    x
    		)
    =
    0
Question 22
22.
    • Solve the equation
    • (
      x
      +
      7
      		)
      =
      0
  • (i)
    -10
  • (ii)
    -6
  • (iii)
    -7
  • (iv)
    -8
  • (v)
    -4
Question 23
23.
    • In an examination, the ratio of passes to failures was 7 : 4.
    • Had 130 less appeared and 15 less passed, the ratio of passes to failures would have been 81 : 25.
    • How many students appeared for the examination?
  • (i)
    650
  • (ii)
    670
  • (iii)
    665
  • (iv)
    655
  • (v)
    660
Question 24
24.
    • Which of the following equations is the same as
    • (
      3
      x
      −
      4
      		)
      =
      7
  • (i)
    (
    3
    x
    −
    3
    		)
    =
    12
  • (ii)
    (
    3
    x
    +
    1
    		)
    =
    11
  • (iii)
    (
    3
    x
    +
    5
    		)
    =
    12
  • (iv)
    (
    3
    x
    +
    1
    		)
    =
    13
  • (v)
    (
    3
    x
    +
    1
    		)
    =
    12
Question 25
25.
    • Which of the following equations is not the same as
    • (
      6
      x
      +
      1
      		)
      =
      0
  • (i)
    (
    −
    18
    x
    −
    3
    		)
    =
    (
    −
    3
    		)
  • (ii)
    (
    −
    24
    x
    −
    4
    		)
    =
    0
  • (iii)
    (
    18
    x
    +
    3
    		)
    =
    0
  • (iv)
    (
    30
    x
    +
    5
    		)
    =
    0
  • (v)
    (
    12
    x
    +
    2
    		)
    =
    0
    Assignment Key
  •  1) (iv)
  •  2) (ii)
  •  3) (v)
  •  4) (ii)
  •  5) (i)
  •  6) (iv)
  •  7) (iii)
  •  8) (iv)
  •  9) (v)
  •  10) (iv)
  •  11) (v)
  •  12) (iii)
  •  13) (iii)
  •  14) (iii)
  •  15) (v)
  •  16) (v)
  •  17) (iv)
  •  18) (v)
  •  19) (iii)
  •  20) (i)
  •  21) (iv)
  •  22) (iii)
  •  23) (v)
  •  24) (v)
  •  25) (i)