1. Simultaneous Equations
20 May, 2019
Let me explain. If you have an equation like:
x + y = 5,
there are lots of answers.
What are simultaneous equations

2. x + y = 5 x = 4 y = 1 4 + 1 = 5 x = 3 y = 2 3 + 2 = 5 x = 2 y = 3
Here are some of these answers
x + y = 5
x = 4
y = 1
4 + 1 = 5
x = 3
y = 2
3 + 2 = 5
x = 2
y = 3
2 + 3 = 5
x = 1
y = 4
1 + 4 = 5
I can think of some more because
= 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. x + y = 5
x – y = 1
The only values that will fit both equations are x = 3 and y = 2.
Equations like this are called simultaneous equations.
3 + 2 = 5
3 – 2 = 1

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

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

8. Here is a method for solving simultaneous equations
x + y = 9
x – y = 5
2x = 14
x = 7
Make sure that the middles are the same
If the signs are different ADD
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
7 + y = 9
y = 9 – 7
y = 2
Here is a method for solving simultaneous equations
Make sure that the middles are the same
If the signs are different ADD
Find the value of x
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 2x + x = 3x (+ y) + (– y ) = 0
Make sure that the middles are the same
If the signs are different ADD
2x + x = 3x
(+ y) + (– y ) = 0
= 15

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

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

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

17. Make sure that the middles are the same
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