11 x1 t01 09 simultaneous equations (2013)
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Transcript of 11 x1 t01 09 simultaneous equations (2013)
![Page 1: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/1.jpg)
Simultaneous Equations
![Page 2: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/2.jpg)
Simultaneous Equations1) Eliminate a variable
![Page 3: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/3.jpg)
Simultaneous Equations1) Eliminate a variable
2) Solve for the other variable
![Page 4: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/4.jpg)
Simultaneous Equations1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
![Page 5: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/5.jpg)
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
![Page 6: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/6.jpg)
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
![Page 7: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/7.jpg)
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
![Page 8: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/8.jpg)
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
![Page 9: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/9.jpg)
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
![Page 10: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/10.jpg)
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
![Page 11: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/11.jpg)
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
![Page 12: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/12.jpg)
2 2
( ) 2 14 (1)9 (2)
ii x yx y
![Page 13: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/13.jpg)
2 2
( ) 2 14 (1)9 (2)
ii x yx y
Make y the subject in (1)14 2y x
![Page 14: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/14.jpg)
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
![Page 15: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/15.jpg)
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
![Page 16: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/16.jpg)
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
![Page 17: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/17.jpg)
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
![Page 18: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/18.jpg)
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
![Page 19: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/19.jpg)
( ) 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
![Page 20: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/20.jpg)
( ) 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
![Page 21: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/21.jpg)
( ) 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
![Page 22: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/22.jpg)
( ) 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
![Page 23: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/23.jpg)
( ) 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
![Page 24: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/24.jpg)
( ) 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
![Page 25: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/25.jpg)
( ) 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
![Page 26: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/26.jpg)
( ) 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
![Page 27: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/27.jpg)
( ) 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
![Page 28: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/28.jpg)
( ) 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
![Page 29: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/29.jpg)
3 2 10z
44
zz
![Page 30: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/30.jpg)
3 2 10z
44
zz
2 2 4 5x 3x
![Page 31: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/31.jpg)
3 2 10z
44
zz
2 2 4 5x 3x
3, 2, 4x y z
![Page 32: 11 x1 t01 09 simultaneous equations (2013)](https://reader033.fdocuments.in/reader033/viewer/2022052700/55a0a0b51a28abe12f8b470d/html5/thumbnails/32.jpg)
3 2 10z
44
zz
2 2 4 5x 3x
3, 2, 4x y z
Exercise 1H; 1bg, 2cfil, 3aceg, 4aegh, 5a,6ace, 7ad, 8*b, 9***