1. Simultaneous Equations 8 January, 2016 What are simultaneou s equations Let me explain. If you have an equation like: x + y = 5, there are lots of answers.

2. Here are some of these answers x + y = 5 x = 4y = 14 + 1 = 5 x + y = 5 x = 3y = 23 + 2 = 5 x + y = 5 x = 2y = 32 + 3 = 5 x + y = 5 x = 1y = 41 + 4 = 5 I can think of some more because 1.5 + 3.5 = 5 so x = 1.5 and y = 3.5 etc.

3. There are lots of answers that fit the equation x + y = 5 That’s right but suppose that we have another equation to go with x + y = 5 and the x and y must be the same numbers for both equations. x + y = 5 x – y = 1 Like this

4. The only values that will fit both equations are x = 3 and y = 2. Equations like this are called simultaneous equations. x + y = 5 x – y = 1 3 + 2 = 5 3 – 2 = 1

5. Here is a method for solving simultaneous equations x + y = 9 x – y = 5 1.Make sure that the middles are the same y

6. Here is a method for solving simultaneous equations x + y = 9 x – y = 5 1.Make sure that the middles are the same 2.If the signs are different ADD (+ y) and (– y) have different signs so ADD

7. Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 1.Make sure that the middles are the same 2.If the signs are different ADD x + x = 2x and (+ y ) + (- y ) = 0 and 9 + 5 = 14

8. Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 x = 7 1.Make sure that the middles are the same 2.If the signs are different ADD 3.Find the value of x 2 x = 14 x = 14 ÷ 2 x = 7

9. Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 x = 7 x + y = 9 7 + y = 9 y = 9 – 7 y = 2 1.Make sure that the middles are the same 2.If the signs are different ADD 3.Find the value of x 4.Use this to find the value of y 7 + y = 9 y = 9 – 7 y = 2

10. Here is another pair of simultaneous equations 2x + y = 11 x – y = 4 To solve, follow the steps

11. 2x + y = 11 x – y = 4 3x = 15 1.Make sure that the middles are the same 2.If the signs are different ADD 2x + x = 3x (+ y) + (– y ) = 0 11 + 4 = 15

12. 2x + y = 11 x – y = 4 3x = 15 x = 5 1.Make sure that the middles are the same 2.If the signs are different ADD 3.Find the value of x 3x = 15 x = 15 ÷ 3 x = 5

13. 2x + y = 11 x – y = 4 3x = 15 x = 5 2x + y = 11 10 + y = 11 1.Make sure that the middles are the same 2.If the signs are different ADD 3.Find the value of x 4.Use this to find the value of y

14. 2x + y = 11 x – y = 4 3x = 15 x = 5 2x + y = 11 10 + y = 11 y = 11 – 10 y = 1 1.Make sure that the middles are the same 2.If the signs are different ADD 3.Find the value of x 4.Use this to find the value of y

15. When the middle signs are the same 2x + y = 14 x + y = 4 The same

16. 2x + y = 14 x + y = 9 x = 5 2x + y = 14 10 + y = 14 y = 14 – 10 y = 4 1.Make sure that the middles are the same 2.If the signs are the same SUBTRACT 3.Find the value of x 4.Use this to find the value of y

17. 1.Make sure that the middles are the same 2.If the signs are the Same SUBTRACT If the signs are Different ADD 3. Find the value of x 4. Use this to find the value of y