ICSE Board Practice

ICSE Grade VIII - Simultaneous Linear Equations
Question 1
1.
    • Solve the following pair of equations :
    •    
       
       
      4

       
       
      (
      x
      +
      6
      )
         
       
       
      1

       
       
      (
      y
      +
      9
      )
      =
       
       
      (
      27
      )
    •  
       
      14

       
       
      (
      x
      +
      6
      )
        +  
       
       
      7

       
       
      (
      y
      +
      9
      )
      =
       
       
      77
  • (
    (
    -47

    8
    )
    ,
    (
    -46

    5
    )
    )
  • (
    1
    ,
    (
    -46

    5
    )
    )
  • (
    (
    -47

    8
    )
    ,
    -3
    )
  • (
    3
    ,
    (
    -46

    5
    )
    )
  • (
    (
    -47

    8
    )
    ,
    -1
    )
Question 2
2.
    • Solve the following pair of equations :
    •    
       
       
      3

       
       
      (
      4
      x
      +
      y
      )
         
       
       
      4

       
       
      (
      4
      x
      y
      )
      =
       
       
      6
    •  
       
      8

       
       
      (
      4
      x
      +
      y
      )
         
       
       
      7

       
       
      (
      4
      x
      y
      )
      =
       
       
      37
  • (
    1

    50
    ,
    5

    12
    )
  • (
    1

    16
    ,
    5

    12
    )
  • (
    1

    48
    ,
    1

    2
    )
  • (
    1

    48
    ,
    5

    12
    )
  • (
    1

    48
    ,
    1

    4
    )
Question 3
3.
    • 5
    • men and
    • 16
    • women can do a piece of work in
    • 6
    • days.
    • 3
    • men and
    • 4
    • women can do the same work in
    • 10
    • days.
    • In how many days can
    • 2
    • men and
    • 5
    • women complete the same work?
  • 16
    days
  • 17
    days
  • 14
    days
  • 13
    days
  • 15
    days
Question 4
4.
    • Solve
    • (
      4
      x
      5
      y
      5
      )
      =
      (
      x
      +
      5
      y
      3
      )
      (
      x
      +
      4
      y
      2
      )
      =
      (
      4
      x
      +
      2
      y
      4
      )
  • (
    (
    -4

    17
    )
    ,
    (
    -1

    3
    )
    )
  • (
    (
    -2

    15
    )
    ,
    -1
    )
  • (
    (
    -4

    17
    )
    ,
    -1
    )
  • (
    (
    -4

    15
    )
    ,
    (
    -1

    3
    )
    )
Question 5
5.
    • Solve the following pair of equations :
    •    
       
       
      4

       
       
      x
         
       
       
      6

       
       
      y
      =
       
       
      (
      40
      )
    •  
       
      1

       
       
      x
         
       
       
      7

       
       
      y
      =
       
       
      (
      58
      )
  • (
    (
    -1

    2
    )
    ,
    1

    6
    )
  • (
    1
    ,
    1

    8
    )
  • (
    (
    -1

    2
    )
    ,
    1

    8
    )
  • (
    (
    -3

    2
    )
    ,
    1

    8
    )
  • (
    (
    -1

    2
    )
    ,
    (
    -1

    8
    )
    )
Question 6
6.
    • Solve the following pair of equations :
    •    
       
       
      11

       
       
      (
      x
      +
      y
      )
         
       
       
      1

       
       
      (
      x
      y
      )
      =
       
       
      95
    •    
       
       
      5

       
       
      (
      x
      +
      y
      )
         
       
       
      17

       
       
      (
      x
      y
      )
      =
       
       
      (
      23
      )
  • (
    5

    72
    ,
    (
    -13

    70
    )
    )
  • (
    7

    72
    ,
    (
    -13

    72
    )
    )
  • (
    5

    74
    ,
    (
    -13

    72
    )
    )
  • (
    5

    72
    ,
    (
    -13

    72
    )
    )
  • (
    5

    72
    ,
    (
    -5

    24
    )
    )
Question 7
7.
A motor boat can travel at a speed of 18.64 m/sec downstream and 0.28 m/sec upstream. What is the speed of the motor boat in still water?
  • 10.46 m/sec
  • 9.46 m/sec
  • 7.46 m/sec
  • 8.46 m/sec
  • 11.46 m/sec
Question 8
8.
    • Solve the following pair of equations :
    •  
       
      4

       
       
      x
        +  
       
       
      2
      y
      =
       
       
      14
    •    
       
       
      11

       
       
      x
         
       
       
      y
      =
       
       
      (
      16
      )
  • (
    2
    ,
    5
    )
  • (
    1

    1
    ,
    4
    )
  • (
    1

    1
    ,
    3
    )
  • (
    1

    1
    ,
    5
    )
  • (
    3
    ,
    5
    )
Question 9
9.
A motor boat can travel at a speed of 40.41 m/sec downstream and 15.91 m/sec upstream. How much time will it take to cross a distance of 380.72 m in still water?
  • 11.52 sec
  • 12.52 sec
  • 13.52 sec
  • 14.52 sec
  • 15.52 sec
Question 10
10.
    • Solve the following pair of equations :
    •  
       
      4
      x
         
       
       
      11

       
       
      y
      =
       
       
      17
    •  
       
      x
         
       
       
      5

       
       
      y
      =
       
       
      11
  • (
    -4
    ,
    (
    -1

    5
    )
    )
  • (
    -4
    ,
    1

    3
    )
  • (
    -1
    ,
    (
    -1

    3
    )
    )
  • (
    -3
    ,
    (
    -1

    3
    )
    )
  • (
    -4
    ,
    (
    -1

    3
    )
    )