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Simultaneous Equations 2x + 3y = 12 x + y = 5
Aims for this topic: ,[object Object],[object Object],[object Object]
What are simultaneous equations? ,[object Object],[object Object],[object Object],x + 2 = 8
What are simultaneous equations? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],x + y = 5
What are simultaneous equations? ,[object Object],[object Object],[object Object],x + y = 5 2x + 3y = 12
What are simultaneous equations? ,[object Object],[object Object],x + y = 5 2x + 3y = 12
How do you solve simultaneous equations? ,[object Object],[object Object],[object Object]
Solving simultaneous equations using graphs ,[object Object],[object Object],[object Object],[object Object]
Solving simultaneous equations using graphs ,[object Object],[object Object],[object Object],[object Object]
1. Do a table of values for each equation: ,[object Object],x + 2y = 4 0.5 1 1.5 2 2.5 3 3.5 y 3 2 1 0 -1 -2 -3 X 0 1 2 3 4 5 6 y 3 2 1 0 -1 -2 -3 X
2. Draw the two graphs:
3. Write down the x and y values where the graphs cross  : The lines cross where x = 2 and y =1
Solving simultaneous equations algebraically ,[object Object],[object Object],ELIMINATE!
Solving simultaneous equations by elimination ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Solving simultaneous equations by elimination ,[object Object],[object Object],[object Object],[object Object],[object Object]
1. Organise your equations ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
2. Make Sure Two Coefficients are Equal  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
3. Eliminate a Letter ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
4. Solve the equation ,[object Object],[object Object],[object Object],[object Object],[object Object]
5. Substitute ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
6. Don’t forget to check your answer! ,[object Object],[object Object],[object Object]
Just checking: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Remember the six steps for the elimination method: ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Simultaneous Equations