11 x1 t01 09 simultaneous equations (2013)

Download 11 x1 t01 09 simultaneous equations (2013)

Post on 11-Jul-2015

396 views

Category:

Education

0 download

Embed Size (px)

TRANSCRIPT

  • Simultaneous Equations

  • Simultaneous Equations1) Eliminate a variable

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    3) Substitute to find the eliminated variable

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    3) Substitute to find the eliminated variable

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    3) Substitute to find the eliminated variable

    Multiply (1) by 2 and (2) by 3

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    4 6 4215 6 9

    x yx y

    3) Substitute to find the eliminated variable

    Multiply (1) by 2 and (2) by 3

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    4 6 4215 6 9

    x yx y

    11 = 33x

    3) Substitute to find the eliminated variable

    Multiply (1) by 2 and (2) by 3

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    4 6 4215 6 9

    x yx y

    11 = 33x

    3) Substitute to find the eliminated variable

    Multiply (1) by 2 and (2) by 3

    = 3x

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    4 6 4215 6 9

    x yx y

    11 = 33x

    3) Substitute to find the eliminated variable

    Multiply (1) by 2 and (2) by 3

    = 3x 2 3 3 21y

    3 279

    yy

  • Simultaneous Equations1) Eliminate a variable

    2) Solve for the other variable

    e.g. ( ) 2 3 21 (1)5 2 3 (2)

    i x yx y

    4 6 4215 6 9

    x yx y

    11 = 33x

    3) Substitute to find the eliminated variable

    Multiply (1) by 2 and (2) by 3

    = 3x 2 3 3 21y

    3 279

    yy3, 9x y

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

    Make y the subject in (1)14 2y x

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

    Make y the subject in (1)14 2y x

    Substitute into (2) 22 14 2 9x x

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

    Make y the subject in (1)14 2y x

    Substitute into (2) 22 14 2 9x x

    2 2

    2

    196 56 4 93 56 205 0

    x x xx x

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

    Make y the subject in (1)14 2y x

    Substitute into (2) 22 14 2 9x x

    2 2

    2

    196 56 4 93 56 205 0

    x x xx x

    3 41 5 0x x 415 or 3

    x x

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

    Make y the subject in (1)14 2y x

    Substitute into (2) 22 14 2 9x x

    2 2

    2

    196 56 4 93 56 205 0

    x x xx x

    3 41 5 0x x 415 or 3

    x x

    412 5 14 or 2 143

    404 or 3

    y y

    y y

  • 2 2

    ( ) 2 14 (1)9 (2)

    ii x yx y

    Make y the subject in (1)14 2y x

    Substitute into (2) 22 14 2 9x x

    2 2

    2

    196 56 4 93 56 205 0

    x x xx x

    3 41 5 0x x 415 or 3

    x x

    412 5 14 or 2 143

    404 or 3

    y y

    y y

    41 405, 4 or ,3 3

    x y x y

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

    Multiply (1) by 4

    4 8 4 204 5 3 10

    x y zx y z

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

    Multiply (1) by 4

    4 8 4 204 5 3 10

    x y zx y z

    3 10y z

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

    Multiply (1) by 4

    4 8 4 204 5 3 10

    x y zx y z

    3 10y z Solve these new equations simultaneously

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

    Multiply (1) by 4

    4 8 4 204 5 3 10

    x y zx y z

    3 10y z Solve these new equations simultaneously

    7 6 3818 6 60

    y zy z

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

    Multiply (1) by 4

    4 8 4 204 5 3 10

    x y zx y z

    3 10y z Solve these new equations simultaneously

    7 6 3818 6 60

    y zy z

  • ( ) 2 5 (1)2 3 4 28 (2)4 5 3 10 (3)

    iii x y zx y zx y z

    any time you have the same number of pronumerals as equations it should

    be possible to find their values Create two pairs of two equations and eliminate the same variable from both

    Multiply (1) by 2

    2 4 2 102 3 4 28

    x y zx y z

    7 6 38y z

    Multiply (1) by 4

    4 8 4 204 5 3 10

    x y zx y z

    3 10y z Solve these new equations simultaneously

    7 6 3818 6 60

    y zy z

    11 22 2

    yy

  • 3 2 10z 4

    4zz

  • 3 2 10z 4

    4zz

    2 2 4 5x 3x

  • 3 2 10z 4

    4zz

    2 2 4 5x 3x

    3, 2, 4x y z

  • 3 2 10z 4

    4zz

    2 2 4 5x 3x

    3, 2, 4x y z

    Exercise 1H; 1bg, 2cfil, 3aceg, 4aegh, 5a,6ace, 7ad, 8*b, 9***

    Slide Number 1Slide Number 2Slide Number 3Slide Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number 8Slide Number 9Slide Number 10Slide Number 11Slide Number 12Slide Number 13Slide Number 14Slide Number 15Slide Number 16Slide Number 17Slide Number 18Slide Number 19Slide Number 20Slide Number 21Slide Number 22Slide Number 23Slide Number 24Slide Number 25Slide Number 26Slide Number 27Slide Number 28Slide Number 29Slide Number 30Slide Number 31Slide Number 32