1. Simultaneous Equations

2. Simultaneous Equations
1) Eliminate a variable

3. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable

4. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable

5. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)

6. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)
Multiply (1) by 2 and (2) by 3

7. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)
Multiply (1) by 2 and (2) by 3
4 x  6 y  42
15 x  6 y  9

8. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)
Multiply (1) by 2 and (2) by 3
4 x  6 y  42
15 x  6 y  9
11x =  33

9. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)
Multiply (1) by 2 and (2) by 3
4 x  6 y  42
15 x  6 y  9
11x =  33
x = 3

10. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)
Multiply (1) by 2 and (2) by 3
4 x  6 y  42
15 x  6 y  9
11x =  33  2  3  3 y  21
x = 3 3 y  27
y9

11. Simultaneous Equations
1) Eliminate a variable
2) Solve for the other variable
3) Substitute to find the eliminated variable
e.g. (i ) 2 x  3 y  21 (1)
5 x  2 y  3  (2)
Multiply (1) by 2 and (2) by 3
4 x  6 y  42
15 x  6 y  9
11x =  33  2  3  3 y  21
x = 3 3 y  27
y9
 x  3, y  9

12. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)

13. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)
Make y the subject in (1)
y  14  2 x

14. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)
Make y the subject in (1)
y  14  2 x
Substitute into (2)
x 2  14  2 x   9
2

15. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)
Make y the subject in (1)
y  14  2 x
Substitute into (2)
x 2  14  2 x   9
2
x 2  196  56 x  4 x 2  9
3 x 2  56 x  205  0

16. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)
Make y the subject in (1)
y  14  2 x
Substitute into (2)
x 2  14  2 x   9
2
x 2  196  56 x  4 x 2  9
3 x 2  56 x  205  0
 3x  41 x  5   0
41
x  5 or x 
3

17. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)
Make y the subject in (1)
y  14  2 x
Substitute into (2)
x 2  14  2 x   9
2
x 2  196  56 x  4 x 2  9
3 x 2  56 x  205  0
 3x  41 x  5   0
41
x  5 or x 
3
 41    14
2  5   y  14 or 2   y
3
40
y  4 or y  
3

18. (ii ) 2 x  y  14 (1)
x 2  y 2  9  (2)
Make y the subject in (1)
y  14  2 x
Substitute into (2)
x 2  14  2 x   9
2
x 2  196  56 x  4 x 2  9
3 x 2  56 x  205  0
 3x  41 x  5   0
41
x  5 or x 
3
 41    14
2  5   y  14 or 2   y
3
41 40
40  x  5, y  4 or x  , y  
y  4 or y   3 3
3

19. (iii ) x  2 y  z  5  (1)
2 x  3 y  4 z  28  (2) any time you have the same number of
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values

20. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both

21. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2
2 x  4 y  2 z  10
2 x  3 y  4 z  28

22. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2
2 x  4 y  2 z  10
2 x  3 y  4 z  28
7 y  6 z  38

23. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2 Multiply (1) by 4
2 x  4 y  2 z  10 4 x  8 y  4 z  20
2 x  3 y  4 z  28 4 x  5 y  3 z  10
7 y  6 z  38

24. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2 Multiply (1) by 4
2 x  4 y  2 z  10 4 x  8 y  4 z  20
2 x  3 y  4 z  28 4 x  5 y  3 z  10
7 y  6 z  38 3 y  z  10

25. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2 Multiply (1) by 4
2 x  4 y  2 z  10 4 x  8 y  4 z  20
2 x  3 y  4 z  28 4 x  5 y  3 z  10
7 y  6 z  38 3 y  z  10
Solve these new equations simultaneously

26. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2 Multiply (1) by 4
2 x  4 y  2 z  10 4 x  8 y  4 z  20
2 x  3 y  4 z  28 4 x  5 y  3 z  10
7 y  6 z  38 3 y  z  10
Solve these new equations simultaneously
7 y  6 z  38
18 y  6 z  60

27. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2 Multiply (1) by 4
2 x  4 y  2 z  10 4 x  8 y  4 z  20
2 x  3 y  4 z  28 4 x  5 y  3 z  10
7 y  6 z  38 3 y  z  10
Solve these new equations simultaneously
7 y  6 z  38
18 y  6 z  60

28. (iii ) x  2 y  z  5  (1)
any time you have the same number of
2 x  3 y  4 z  28  (2)
pronumerals as equations it should
4 x  5 y  3 z  10 (3) be possible to find their values
Create two pairs of two equations and
eliminate the same variable from both
Multiply (1) by 2 Multiply (1) by 4
2 x  4 y  2 z  10 4 x  8 y  4 z  20
2 x  3 y  4 z  28 4 x  5 y  3 z  10
7 y  6 z  38 3 y  z  10
Solve these new equations simultaneously
7 y  6 z  38
18 y  6 z  60
11 y  22
y  2

29.  3  2   z  10
 z  4
z4

30.  3  2   z  10  x  2  2   4  5
 z  4 x3
z4

31.  3  2   z  10  x  2  2   4  5
 z  4 x3
z4
 x  3, y  2, z  4

32.  3  2   z  10  x  2  2   4  5
 z  4 x3
z4
 x  3, y  2, z  4
Exercise 1H; 1bg, 2cfil, 3aceg, 4aegh, 5a,
6ace, 7ad, 8*b, 9***