# 11 x1 t01 09 simultaneous equations (2013)

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• 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***

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