1. SOLUTION TO SIMULTANEOUS LINEAR EQUATIONS
By Olowolafe Samuel Opeyemi(Opsam)

2. A variable in Mathematics can assume different values
It is usually the unknown which we denote using letters
A linear expression is a Mathematical statement which has the highest power of its variable(s) as E.g. 2x + 5y, a + 2p, -7c – d, etc.
Solution To Simultaneous Linear Equations

3. Solution To Simultaneous Equations

4. c – f = -4, 6v – 5r = 3, 7y + t – 3 = 0, 4e + 3 = 0, etc.
A linear equation is an equation with the highest power of its unknown as E.g.
c – f = -4,
6v – 5r = 3,
7y + t – 3 = 0,
4e + 3 = 0, etc. .
Solution To Simultaneous Linear Equations

5. Simultaneous linear equations are two or more linear equations with at least two variables(unknowns) which could be solved at the same time.
Simultaneous equations could be solved using graphical, elimination, substitution, Crammer, row reduction methods and many more
Solution To Simultaneous Equations

6. Put x = 2 in (ii) USING THE ELIMINATION METHOD-Case 1
Put x = 2 in (ii)
Solution To Simultaneous Linear Equations

7. 2 + y = 5
In conclusion, x = 2 and y = 3

8. x = 2 Put x = 2 in equation ii USING THE ELIMINATION METHOD- Case 1
x = 2
Divide both sides by 6
Put x = 2 in equation ii
Solution To Simultaneous Linear Equations

9. In conclusion, x = 2 and y = -2
In conclusion, x = 2 and y = -2
Solution To Simultaneous Equations

10. a = 4 USING THE ELIMINATION METHOD- Case 1 Put a = 4 in equation ii
Divide both sides by 8
a = 4
Put a = 4 in equation ii

11. Divide both sides by 3

12. Exercise 1: Solve simultaneously using elimination method
Solution To Simultaneous Equations

13. x = 1/2, y = 7/2 x = -4, y = -5 p = 4, q = 22 m = 3, n = -7
ANSWERS TO EXERCISE 1
x = 1/2, y = 7/2
x = -4, y = -5
p = 4, q = 22
m = 3, n = -7
a = -3, b = 4
Solution To Simultaneous Equations

14. USING THE ELIMINATION METHOD- Case 2
X 5
X 6

15. Divide both sides by 52
Solution To Simultaneous Equations

17. 6p = 3 p = 3/6; p = 1/2 Divide both sides by 6
6p = 3
Divide both sides by 6
p = 3/6; p = 1/2
Solution To Simultaneous Equations

18. USING THE ELIMINATION METHOD- Case 2
X 2
X 3

19. Divide both sides by -7
Solution To Simultaneous Equations

20. Collect like terms Put y = 1/7 in equation (ii)
Collect like terms
Solution To Simultaneous Equations

21. 14x = 20 Divide both sides by 14 Cross multiply
Cross multiply
14x = 20
Divide both sides by 14
Solution To Simultaneous Equations

22. USING THE ELIMINATION METHOD- Case 2
X 6
X -3

23. Divide both sides by 9
Put y = 4/9 in equation (i)

24. Collect like terms

25. Cross multiply
-27x = 20
Divide both sides by - 27

26. Exercise 2: Solve simultaneously using elimination method
Solution To Simultaneous Equations

27. ANSWERS TO EXERCISE 2

28. USING THE SUBSTITUTION METHOD- CASE 1 AND 2
From (ii), make y the subject of the formula

29. Put (iii) in (i) that is substitute y = 2 – 7x in (i)
Collect like terms
Solution To Simultaneous Equations

30. Put x = 3 in (iii)
We can finally conclude that x = 3 and y = -19

31. USING THE SUBSTITUTION METHOD- CASE 1 AND 2
From (i), make n the subject of the formula

32. Put (iii) in (ii) that is substitute n = 7m – 15 in (ii)
Put (iii) in (ii) that is substitute n = 7m – 15 in (ii)
Collect like terms
Solution To Simultaneous Equations

33. We can finally conclude that m = 1 and n = -8
Put m = 1 in (iii)
We can finally conclude that m = 1 and n = -8

34. From (i), make a the subject of the formula
From (i), make a the subject of the formula

35. Divide both sides by 2
Solution To Simultaneous Equations

37. Cross multiply
Collect like terms

38. Put b = -4 in (iii)

39. Solution To Simultaneous Equations

40. EXERCISE 3
Use the substitution method to solve the following simultaneous equations

41. Solution To Exercise 3

42. THANK YOU FOR YOUR TIME 2348073801660 opsam911@yahoo.com
FOR ANY ENQUIRY/CONTRIBUTION, YOU CAN CONTACT OPSAM THROUGH:
Solution To Simultaneous Equations