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MODUL 1
      SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT’
             TOPIC : SIMULTANEOUS LINEAR EQUATIONS
                           TIME : 2 HOUR

1. Calculate the values of m and n that satisfy the simultaneous linear equations:
   4m + n = 2 and 2m – 3n = 8                                                    [ 4 marks]




2. Calculate the values of m and n that satisfy the simultaneous linear equations:
      1
        m - 3n = 10
      2
      5m + 6n = -8                                                                   [ 4 marks]




3. Calculate the values of m and n that satisfy the simultaneous linear equations:
      2m – n = 7
      m – 2n = 5                                                                [ 4 marks]
4. Calculate the values of p and q that satisfy the simultaneous linear equations:
      p + 2q = 6
      3
        p – q = -7
      2
                                                                                  [ 4 marks]




5. Calculate the values of m and n that satisfy the simultaneous linear equations:
   4m - 3n = 7 and m + 6n = 4                                                    [ 4 marks]




6. Calculate the values of p and q that satisfy the simultaneous linear equations:
      2p - 3q = 13
      4p + q = 5                                                                   [ 4 marks]
7. Calculate the values of p and q that satisfy the simultaneous linear equations:
       1
         p – 2q = 13
       2
      3p + 4q = -2                                                               [ 4 marks]




8. Calculate the values of k and w that satisfy the simultaneous linear equations:
   2k – 3w = 10 and 4k + w = -1                                                    [ 4 marks]




9. Calculate the values of m and n that satisfy the simultaneous linear equations:
   2m - 5n = -12 and 3m + n = -1                                                 [ 4 marks]
10. Calculate the values of x and y that satisfy the simultaneous linear equations:
      x – 3y = 5
      3x – y = 3                                                                  [ 4 marks]




11. Calculate the values of s and t that satisfy the simultaneous linear equations:
      8s + 3t = 12
      6s – 9t = 24                                                                [ 4 marks]




12. Calculate the values of m and n that satisfy the simultaneous linear equations:
    m - 3n = 6 and 2m – n = 7                                                    [ 4 marks]
13. Calculate the values of k and h that satisfy the simultaneous linear equations:
      4k - 3h = 10
     2k – 5h = 12                                                                [ 4 marks]




14. Calculate the values of m and n that satisfy the simultaneous linear equations:
     2m + 3n = 9
      1
        m–n=2                                                                   [ 4 marks]
      3




15. Calculate the values of m and n that satisfy the simultaneous linear equations:
       2m – n = 2
       4m – 3n = 5                                                              [ 4 marks]
MODULE 1- ANSWERS
                TOPIC: SIMULTENOUS LINEAR EQUATIONS

1. Calculate the values of m and n that satisfy the simultaneous linear equations:
   4m + n = 2 and 2m – 3n = 8                                                    [ 4 marks]


   12m + 3n = 6                                1
    2m – 3n = 8
       14m = 14                                1
         m=1                                   1

          n = -2                               1

2. Calculate the values of m and n that satisfy the simultaneous linear equations:
      1
        m - 3n = 10
      2
      5m + 6n = -8                                                                   [ 4 marks]

      m - 6n = 20                              1
      5m + 6n = -8
           6m = 12                             1
            m=2                                1

          n =-2                                1


3. Calculate the values of m and n that satisfy the simultaneous linear equations:
      2m – n = 7
      m – 2n = 5                                                                [ 4 marks]

      2m – n = 7
      2m – 4n = 10                              1
          3n = -3                               1
           n = -1                               1

            m =3                                1

4. Calculate the values of p and q that satisfy the simultaneous linear equations:
      p + 2q = 6
      3
        p – q = -7
      2
                                                                                 [ 4 marks]

      p + 2q = 6
      3p – 2q = -14                            1
            4p= -8                             1
             p = -2                            1
             q =4                              1
5. Calculate the values of m and n that satisfy the simultaneous linear equations:
   4m - 3n = 7 and m + 6n = 4                                                    [ 4 marks]


   4m - 3n = 7
   4m + 24n = 16                                1
       -27n = -9                                1
                1
          n=                                    1
                3

          m =2                                  1


6. Calculate the values of p and q that satisfy the simultaneous linear equations:
      2p - 3q = 13
      4p + q = 5                                                                   [ 4 marks]

      4p - 6q = 26                              1
      4p + q = 5
        -7q = 21                                1
         q = -3                                 1

          p =2                                  1

7. Calculate the values of p and q that satisfy the simultaneous linear equations:
       1
         p – 2q = 13
       2
      3p + 4q = -2                                                                [ 4 marks]

       p – 4q = 26                              1
       3p + 4q = -2
        4p = 24                                 1
          p=6                                   1

          q = -5                                1

8. Calculate the values of k and w that satisfy the simultaneous linear equations:
   2k – 3w = 10 and 4k + w = -1                                                    [ 4 marks]

    4k – 6w = 20                                1
    4k + w = -1
        -7w = 21                                1
          w = -3                                1

                1
          k =                                   1
                2
9. Calculate the values of m and n that satisfy the simultaneous linear equations:
   2m - 5n = -12 and 3m + n = -1                                                 [ 4 marks]

    2m - 5n = -12
    15m + 5n = -5                               1
         17m = 17                               1
          m = -1                                1

          n =2                                  1

10. Calculate the values of x and y that satisfy the simultaneous linear equations:
      x – 3y = 5
      3x – y = 3                                                                  [ 4 marks]

      3x – 9y = 15                              1
      3x – y = 3
          -8y = 12                             1
                  3
            y=-                                 1
                  2

                 1
            x=                                  1
                 2

11. Calculate the values of s and t that satisfy the simultaneous linear equations:
      8s + 3t = 12
      6s – 9t = 24                                                                [ 4 marks]

      24s + 9t = 36                             1
      6s – 9t = 24
           30s = 60                             1
              s=2                               1

                     4
              t=-                               1
                     3

12. Calculate the values of m and n that satisfy the simultaneous linear equations:
    m - 3n = 6 and 2m – n = 7                                                    [ 4 marks]

      2m - 6n = 12                              1
      2m - n = 7
       -5n = 5                                  1
         n = -1                                 1

          m =3                                 1
13. Calculate the values of k and h that satisfy the simultaneous linear equations:
      4k - 3h = 10
     2k – 5h = 12                                                                [ 4 marks]


     4k - 3h = 10
     4k – 10h = 24                             1
           -7h = -14                           1
             h=2                               1

            k=4                                1

14. Calculate the values of m and n that satisfy the simultaneous linear equations:
     2m + 3n = 9
      1
        m–n=2                                                                   [ 4 marks]
      3

     2m + 3n = 9
      m – 3n = 6                                1
        3m = 15                                 1
        m= 5                                    1

                1
          n =                                   1
                3


15. Calculate the values of m and n that satisfy the simultaneous linear equations:
       2m – n = 2
       4m – 3n = 5                                                              [ 4 marks]

       6m – 3n = 6                             1
       4m – 3n = 5
            2m = 1                             1
                    1
             m=                                 1
                    2
              n =1                             1

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Intervensi Modul 1 Simutaneous

  • 1. MODUL 1 SKIM TIUSYEN FELDA (STF) MATEMATIK SPM “ENRICHMENT’ TOPIC : SIMULTANEOUS LINEAR EQUATIONS TIME : 2 HOUR 1. Calculate the values of m and n that satisfy the simultaneous linear equations: 4m + n = 2 and 2m – 3n = 8 [ 4 marks] 2. Calculate the values of m and n that satisfy the simultaneous linear equations: 1 m - 3n = 10 2 5m + 6n = -8 [ 4 marks] 3. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m – n = 7 m – 2n = 5 [ 4 marks]
  • 2. 4. Calculate the values of p and q that satisfy the simultaneous linear equations: p + 2q = 6 3 p – q = -7 2 [ 4 marks] 5. Calculate the values of m and n that satisfy the simultaneous linear equations: 4m - 3n = 7 and m + 6n = 4 [ 4 marks] 6. Calculate the values of p and q that satisfy the simultaneous linear equations: 2p - 3q = 13 4p + q = 5 [ 4 marks]
  • 3. 7. Calculate the values of p and q that satisfy the simultaneous linear equations: 1 p – 2q = 13 2 3p + 4q = -2 [ 4 marks] 8. Calculate the values of k and w that satisfy the simultaneous linear equations: 2k – 3w = 10 and 4k + w = -1 [ 4 marks] 9. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m - 5n = -12 and 3m + n = -1 [ 4 marks]
  • 4. 10. Calculate the values of x and y that satisfy the simultaneous linear equations: x – 3y = 5 3x – y = 3 [ 4 marks] 11. Calculate the values of s and t that satisfy the simultaneous linear equations: 8s + 3t = 12 6s – 9t = 24 [ 4 marks] 12. Calculate the values of m and n that satisfy the simultaneous linear equations: m - 3n = 6 and 2m – n = 7 [ 4 marks]
  • 5. 13. Calculate the values of k and h that satisfy the simultaneous linear equations: 4k - 3h = 10 2k – 5h = 12 [ 4 marks] 14. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m + 3n = 9 1 m–n=2 [ 4 marks] 3 15. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m – n = 2 4m – 3n = 5 [ 4 marks]
  • 6. MODULE 1- ANSWERS TOPIC: SIMULTENOUS LINEAR EQUATIONS 1. Calculate the values of m and n that satisfy the simultaneous linear equations: 4m + n = 2 and 2m – 3n = 8 [ 4 marks] 12m + 3n = 6 1 2m – 3n = 8 14m = 14 1 m=1 1 n = -2 1 2. Calculate the values of m and n that satisfy the simultaneous linear equations: 1 m - 3n = 10 2 5m + 6n = -8 [ 4 marks] m - 6n = 20 1 5m + 6n = -8 6m = 12 1 m=2 1 n =-2 1 3. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m – n = 7 m – 2n = 5 [ 4 marks] 2m – n = 7 2m – 4n = 10 1 3n = -3 1 n = -1 1 m =3 1 4. Calculate the values of p and q that satisfy the simultaneous linear equations: p + 2q = 6 3 p – q = -7 2 [ 4 marks] p + 2q = 6 3p – 2q = -14 1 4p= -8 1 p = -2 1 q =4 1
  • 7. 5. Calculate the values of m and n that satisfy the simultaneous linear equations: 4m - 3n = 7 and m + 6n = 4 [ 4 marks] 4m - 3n = 7 4m + 24n = 16 1 -27n = -9 1 1 n= 1 3 m =2 1 6. Calculate the values of p and q that satisfy the simultaneous linear equations: 2p - 3q = 13 4p + q = 5 [ 4 marks] 4p - 6q = 26 1 4p + q = 5 -7q = 21 1 q = -3 1 p =2 1 7. Calculate the values of p and q that satisfy the simultaneous linear equations: 1 p – 2q = 13 2 3p + 4q = -2 [ 4 marks] p – 4q = 26 1 3p + 4q = -2 4p = 24 1 p=6 1 q = -5 1 8. Calculate the values of k and w that satisfy the simultaneous linear equations: 2k – 3w = 10 and 4k + w = -1 [ 4 marks] 4k – 6w = 20 1 4k + w = -1 -7w = 21 1 w = -3 1 1 k = 1 2
  • 8. 9. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m - 5n = -12 and 3m + n = -1 [ 4 marks] 2m - 5n = -12 15m + 5n = -5 1 17m = 17 1 m = -1 1 n =2 1 10. Calculate the values of x and y that satisfy the simultaneous linear equations: x – 3y = 5 3x – y = 3 [ 4 marks] 3x – 9y = 15 1 3x – y = 3 -8y = 12 1 3 y=- 1 2 1 x= 1 2 11. Calculate the values of s and t that satisfy the simultaneous linear equations: 8s + 3t = 12 6s – 9t = 24 [ 4 marks] 24s + 9t = 36 1 6s – 9t = 24 30s = 60 1 s=2 1 4 t=- 1 3 12. Calculate the values of m and n that satisfy the simultaneous linear equations: m - 3n = 6 and 2m – n = 7 [ 4 marks] 2m - 6n = 12 1 2m - n = 7 -5n = 5 1 n = -1 1 m =3 1
  • 9. 13. Calculate the values of k and h that satisfy the simultaneous linear equations: 4k - 3h = 10 2k – 5h = 12 [ 4 marks] 4k - 3h = 10 4k – 10h = 24 1 -7h = -14 1 h=2 1 k=4 1 14. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m + 3n = 9 1 m–n=2 [ 4 marks] 3 2m + 3n = 9 m – 3n = 6 1 3m = 15 1 m= 5 1 1 n = 1 3 15. Calculate the values of m and n that satisfy the simultaneous linear equations: 2m – n = 2 4m – 3n = 5 [ 4 marks] 6m – 3n = 6 1 4m – 3n = 5 2m = 1 1 1 m= 1 2 n =1 1