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
    •  
    • (
      −
      2
      x
      +
      3
      y
      +
      15
      		)
      =
      0
      (
      −
      x
      +
      6
      y
      +
      21
      		)
      =
      0
  • (i)
    (
    1
    ,
    (
    −
    5
    )
    )
  • (ii)
    (
    5
    ,
    (
    −
    1
    )
    )
  • (iii)
    (
    3
    ,
    (
    −
    3
    )
    )
  • (iv)
    (
    2
    ,
    3
    )
  • (v)
    (
    2
    ,
    8
    )
Question 2
2.
    • Solve the equation
    • (
      −
      5
      8
      x
      −
      3
      8
      		)
      =
      0
  • (i)
    -1
  • (ii)
    (
    -3
    7
    		 )
  • (iii)
    (
    -1
    5
    		 )
  • (iv)
    (
    -3
    5
    		 )
Question 3
3.
    • Solve the equation
    • (
      −
      5
      2
      x
      +
      4
      		)
      =
      5
  • (i)
    0
  • (ii)
    (
    -2
    5
    		 )
  • (iii)
    (
    -2
    3
    		 )
  • (iv)
    (
    -4
    5
    		 )
  • (v)
    (
    -2
    7
    		 )
Question 4
4.
    • Solve :
    •  
       
      (
      −
      3
      x
      −
      2
      		)
      		  +  
       
       
      (
      −
      3
      x
      +
      1
      		)
       
       
      10
      =
       
       
      (
      x
      −
      5
      		)
       
       
      2
  • (i)
    1
    7
  • (ii)
    5
    19
  • (iii)
    1
    19
  • (iv)
    3
    19
  • (v)
    3
    17
Question 5
5.
The ratio of two numbers is
2
:
4
and their LCM is 48. Find the numbers.
  • (i)
    24
    		:
    48
  • (ii)
    26
    		:
    52
  • (iii)
    22
    		:
    44
  • (iv)
    20
    		:
    40
  • (v)
    28
    		:
    56
Question 6
6.
    • Solve :
    •  
       
      (
      x
      −
      1
      		)
       
       
      5
      		  +  
       
       
      (
      −
      x
      −
      5
      		)
       
       
      2
      =
       
       
      (
      x
      −
      1
      		)
  • (i)
    (
    -19
    13
    		 )
  • (ii)
    (
    -19
    15
    		 )
  • (iii)
    (
    -15
    11
    		 )
  • (iv)
    (
    -17
    13
    		 )
  • (v)
    (
    -15
    13
    		 )
Question 7
7.
    • Solve the equation
    • (
      x
      +
      8
      		)
      =
      0
  • (i)
    -7
  • (ii)
    -6
  • (iii)
    -10
  • (iv)
    -8
  • (v)
    -9
Question 8
8.
    • Solve :
    •   −  
       
       
      1
       
       
      (
      x
      −
      9
      		)
      		  −  
       
       
      2
       
       
      (
      x
      +
      1
      		)
      =
       
       
      9
       
       
      (
      x
      +
      1
      		)
      		  −  
       
       
      12
       
       
      (
      x
      −
      5
      		)
  • (i)
    299
    31
  • (ii)
    281
    29
  • (iii)
    301
    31
  • (iv)
    317
    33
  • (v)
    297
    31
Question 9
9.
    • Which of the following equations is the same as
    • (
      −
      6
      x
      		)
      =
      8
      x
  • (i)
    (
    −
    18
    x
    		)
    =
    (
    24
    x
    +
    4
    		)
  • (ii)
    (
    −
    18
    x
    		)
    =
    (
    24
    x
    −
    4
    		)
  • (iii)
    (
    −
    18
    x
    +
    2
    		)
    =
    24
    x
  • (iv)
    (
    −
    18
    x
    		)
    =
    24
    x
  • (v)
    (
    −
    18
    x
    −
    2
    		)
    =
    24
    x
Question 10
10.
    • Solve
    • (
      −
      x
      −
      9
      y
      +
      44
      		)
      =
      0
      (
      −
      2
      x
      +
      y
      −
      7
      		)
      =
      0
  • (i)
    (
    0
    ,
    5
    )
  • (ii)
    (
    -1
    ,
    4
    )
  • (iii)
    (
    2
    ,
    5
    )
  • (iv)
    (
    -1
    ,
    5
    )
  • (v)
    (
    -1
    ,
    3
    )
Question 11
11.
    • Find the set of points satisfying the equation
    		•
      x
      =
      (
      −
      8
      		)
  • (i)
    • (
      (
      −
      8
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      9
      )
      ,
      2
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      2
      )
  • (ii)
    • (
      (
      −
      8
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      1
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      2
      )
  • (iii)
    • (
      (
      −
      8
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      0
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      1
      )
    • ,
    • (
      (
      −
      6
      )
      ,
      4
      )
  • (iv)
    • (
      (
      −
      8
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      7
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      1
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      2
      )
  • (v)
    • (
      (
      −
      8
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      (
      −
      1
      )
      )
    • ,
    • (
      (
      −
      10
      )
      ,
      (
      −
      2
      )
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      1
      )
    • ,
    • (
      (
      −
      8
      )
      ,
      2
      )
Question 12
12.
    • Find the set of points satisfying the equation
    		•
      y
      =
      (
      −
      9
      		)
  • (i)
    • (
      (
      −
      2
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      4
      ,
      (
      −
      7
      )
      )
  • (ii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      8
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      )
      )
  • (iii)
    • (
      (
      −
      2
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      10
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      )
      )
  • (iv)
    • (
      (
      −
      2
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      0
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      )
      )
  • (v)
    • (
      (
      −
      2
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      (
      −
      1
      )
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      (
      −
      2
      )
      ,
      (
      −
      11
      )
      )
    • ,
    • (
      1
      ,
      (
      −
      9
      )
      )
    • ,
    • (
      2
      ,
      (
      −
      9
      )
      )
Question 13
13.
    • Which of the following equations is the same as
    • (
      7
      x
      +
      1
      		)
      =
      0
  • (i)
    (
    2
    x
    −
    3
    		)
    =
    (
    −
    5
    x
    −
    4
    		)
  • (ii)
    (
    2
    x
    −
    3
    		)
    =
    (
    5
    x
    +
    4
    		)
  • (iii)
    (
    14
    x
    −
    8
    		)
    =
    (
    −
    7
    x
    +
    9
    		)
  • (iv)
    10
    =
    (
    7
    x
    −
    9
    		)
  • (v)
    (
    12
    x
    +
    5
    		)
    =
    (
    −
    5
    x
    −
    4
    		)
Question 14
14.
    • Which of the following equations is not the same as
    • (
      x
      −
      4
      		)
      =
      (
      −
      1
      		)
  • (i)
    (
    −
    2
    x
    −
    11
    		)
    =
    (
    −
    3
    x
    −
    8
    		)
  • (ii)
    (
    4
    x
    −
    3
    		)
    =
    3
    x
  • (iii)
    (
    4
    x
    +
    3
    		)
    =
    (
    −
    3
    x
    −
    8
    		)
  • (iv)
    (
    4
    x
    +
    3
    		)
    =
    (
    3
    x
    +
    6
    		)
  • (v)
    (
    −
    2
    x
    −
    5
    		)
    =
    (
    −
    3
    x
    −
    2
    		)
Question 15
15.
Which of the following is a linear equation in three variable?
  • (i)
    (
    3
    x
    2
     
    +
    13
    x
    +
    4
    		)
    =
    0
  • (ii)
    (
    7
    x
    +
    y
    −
    5
    z
    −
    9
    		)
    =
    0
  • (iii)
    (
    x
    +
    7
    		)
    =
    0
  • (iv)
    (
    7
    x
    2
     
    −
    18
    x
    y
    +
    8
    x
    −
    9
    y
    2
     
    +
    1
    		)
    =
    0
  • (v)
    (
    −
    8
    x
    −
    y
    +
    9
    		)
    =
    0
Question 16
16.
    • Solve
    •  
    • (
      −
      4
      x
      −
      5
      y
      −
      16
      		)
      =
      0
      (
      −
      16
      x
      −
      20
      y
      −
      64
      		)
      =
      0
  • (i)
    Infinite solutions
  • (ii)
    No solution
  • (iii)
    (
    6
    ,
    (
    −
    5
    )
    )
  • (iv)
    (
    (
    −
    4
    )
    ,
    0
    )
  • (v)
    (
    1
    ,
    (
    −
    4
    )
    )
Question 17
17.
The equation of x-axis is
  • (i)
    y
    =
    x
  • (ii)
    x
    =
    0
  • (iii)
    x
    =
    1
  • (iv)
    y
    =
    1
  • (v)
    y
    =
    0
Question 18
18.
    • Which of the following equations is not the same as
    • (
      −
      x
      −
      8
      		)
      =
      6
  • (i)
    (
    −
    x
    −
    10
    		)
    =
    8
  • (ii)
    (
    −
    x
    −
    9
    		)
    =
    5
  • (iii)
    (
    −
    x
    −
    12
    		)
    =
    2
  • (iv)
    (
    −
    x
    −
    4
    		)
    =
    10
  • (v)
    (
    −
    x
    −
    7
    		)
    =
    7
Question 19
19.
    • Solve :
    •  
       
      5
      x
      		  +  
       
       
      (
      5
      x
      +
      5
      		)
       
       
      2
      =
       
       
      (
      −
      3
      x
      		)
  • (i)
    (
    -1
    7
    		 )
  • (ii)
    (
    -5
    19
    		 )
  • (iii)
    (
    -5
    23
    		 )
  • (iv)
    (
    -5
    21
    		 )
  • (v)
    (
    -1
    3
    		 )
Question 20
20.
    • Which of the following equations is not the same as
    • (
      −
      7
      x
      −
      5
      		)
      =
      (
      −
      9
      x
      −
      3
      		)
  • (i)
    (
    −
    8
    x
    −
    5
    		)
    =
    (
    −
    10
    x
    −
    3
    		)
  • (ii)
    (
    −
    8
    x
    −
    5
    		)
    =
    (
    −
    8
    x
    −
    3
    		)
  • (iii)
    (
    −
    6
    x
    −
    5
    		)
    =
    (
    −
    8
    x
    −
    3
    		)
  • (iv)
    (
    −
    6
    x
    −
    3
    		)
    =
    (
    −
    8
    x
    −
    1
    		)
  • (v)
    (
    −
    8
    x
    −
    7
    		)
    =
    (
    −
    10
    x
    −
    5
    		)
Question 21
21.
    • Which of the displayed lines represent the equation
    • y
      =
      (
      −
      5
      6
      x
      		)
  • (i)
      • line with point
      • S
  • (ii)
      • line with point
      • W
  • (iii)
      • line with point
      • T
  • (iv)
      • line with point
      • U
  • (v)
      • line with point
      • V
Question 22
22.
    • Which of the following equations is the same as
    • 9
      x
      =
      0
  • (i)
    (
    9
    x
    −
    6
    		)
    =
    (
    −
    4
    		)
  • (ii)
    (
    9
    x
    −
    4
    		)
    =
    1
  • (iii)
    (
    9
    x
    −
    4
    		)
    =
    (
    −
    9
    		)
  • (iv)
    (
    9
    x
    −
    2
    		)
    =
    (
    −
    4
    		)
  • (v)
    (
    9
    x
    −
    4
    		)
    =
    (
    −
    4
    		)
Question 23
23.
    • Solve the following pair of equations :
    •   −  
       
       
      2
       
       
      x
      		  +  
       
       
      13
      y
      =
       
       
      8
    •   −  
       
       
      4
       
       
      x
      		  +  
       
       
      9
      y
      =
       
       
      (
      −
      18
      		)
  • (i)
    (
    1
    11
    ,
    2
    )
  • (ii)
    (
    1
    3
    ,
    2
    )
  • (iii)
    (
    1
    9
    ,
    0
    )
  • (iv)
    (
    1
    9
    ,
    2
    )
  • (v)
    (
    1
    9
    ,
    1
    )
Question 24
24.
Which of the following is a linear equation in one variable?
  • (i)
    (
    −
    36
    x
    2
     
    +
    36
    x
    +
    7
    		)
    =
    (
    −
    x
    −
    9
    		)
  • (ii)
    (
    −
    6
    x
    +
    3
    y
    		)
    =
    (
    8
    x
    −
    7
    y
    +
    4
    		)
  • (iii)
    (
    −
    8
    x
    2
     
    +
    48
    x
    y
    +
    28
    x
    −
    54
    y
    2
     
    −
    90
    y
    −
    24
    		)
    =
    0
  • (iv)
    (
    −
    7
    x
    +
    9
    y
    +
    9
    z
    −
    1
    		)
    =
    (
    −
    5
    x
    −
    9
    y
    +
    6
    z
    +
    7
    		)
  • (v)
    (
    3
    x
    −
    3
    		)
    =
    (
    7
    x
    +
    8
    		)
Question 25
25.
    • The point of intersection of x-axis and y-axis
  • (i)
    (
    1
    ,
    1
    )
  • (ii)
    (
    1
    ,
    0
    )
  • (iii)
    (
    0
    ,
    0
    )
  • (iv)
    (
    0
    ,
    7
    )
    Assignment Key
  •  1) (iii)
  •  2) (iv)
  •  3) (ii)
  •  4) (iv)
  •  5) (i)
  •  6) (iv)
  •  7) (iv)
  •  8) (i)
  •  9) (iv)
  •  10) (iv)
  •  11) (ii)
  •  12) (iv)
  •  13) (i)
  •  14) (iii)
  •  15) (ii)
  •  16) (i)
  •  17) (v)
  •  18) (i)
  •  19) (iv)
  •  20) (ii)
  •  21) (i)
  •  22) (v)
  •  23) (iv)
  •  24) (v)
  •  25) (iii)