1. Simultaneous Equations

2. Types- (2 equations)
Linear
Linear & Non Linear
NonLinear

3. Methods
Algebraic
Substitution
Elimination
Graphical
Matrix

4. 2 Linear Equations Graphical Method Algebraic Methods Solutions
Substitution
Elimination
Solutions

5. Substitution
Combine the two equations by substituting one into the other
1. Make one of the variables the subject of one of the equations
2. Substitute the subject into the other equations
The result is that we end up with one equation with one unknown which we can solve for, then:
3. Find the other variable by substituting into a previous equations

6. Substitution
Solve: 𝑥+𝑦=7 𝑥−𝑦=3

7. Substitution
Solve: 3𝑥+𝑦=18 2𝑥−𝑦=7

8. Substitution
Solve: 𝑦=2𝑥−1 𝑦=𝑥+3

9. Substitution
Solve: 3𝑦+4𝑥=2 𝑥−3𝑦=8

10. Substitution
Solve: 4𝑥+2𝑦=5 3𝑥+6𝑦=6

11. Substitution
Solve: 3𝑥−5𝑦=−16 5𝑥+6𝑦=45

12. Elimination
Combine the two equations by adding/subtracting the two equations in such a way that one of the variables is eliminated
1. Make one of the variables have the same coefficient
2. Add ( if the signs are different); subtract (if the signs are different) to eliminate that variable
The result is that we end up with one equation with one unknown which we can solve for, then:
3. Find the other variable by substituting into a previous equations

13. Elimination
Solve: 𝑥+𝑦=7 𝑥−𝑦=3

14. Elimination
Solve: 3𝑥+𝑦=18 2𝑥−𝑦=7

15. Elimination
Solve: 3𝑦+4𝑥=2 𝑥−3𝑦=8

16. Elimination
Solve: 4𝑥+2𝑦=5 3𝑥+6𝑦=6

17. Elimination
Solve: 3𝑥−5𝑦=−16 5𝑥+6𝑦=45

18. Elimination
Solve: 2𝑥−5𝑦=−8 −3𝑥−2𝑦=−26

19. Linear & NonLinear Graphical Method Algebraic Methods Solutions
Substitution
***Elimination
Solutions