Simultaneous Equations

1
Simultaneous Equations
31 December, 2020
Let me explain. If you have an equation like x
y 5, there are lots of answers.
What are simultaneous equations
2
Here are some of these answers
x y 5 x 4 y 1 4 1 5
x y 5 x 3 y 2 3 2 5
x y 5 x 2 y 3 2 3 5
x y 5 x 1 y 4 1 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
Thats 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

• Make sure that the middles are the same
• y
• 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 9 5 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 x y
9 7 y 9 y 9 7 y 2

• 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

• Make sure that the middles are the same
• 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

• 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
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

• 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