Substitution involves replacing values in one equation into another equation to solve for unknown values. The document provides an example of using substitution to solve the equations x=7-y and x=y-3 for values of x and y. Moving values involves changing the signs (e.g. from + to -) of terms when rearranging terms in an equation to solve for a particular variable. The document walks through using substitution and moving values to solve the example equation y-3=7-y.

1. 1.Substitution
Substitution basically refers to putting a value
into another equation in order to find out the
value of a certain number.

2. Example
 If we know 2 things, x=7-y and x=y-3,
we can use substitution to find out the
values of the 2 numbers
 In this case, we can substitute the
value of x from the 2nd equation (y-3)
into the value of x in the first
equation(x+y=7).

3. Example
 We can do this because the 2 “x” are
actually the same value.
 Thus, we can say that y-3=7-y(its
actually the same as saying x=x)
 And that is basically all substitution is
about!

4. 2.Moving of values
 OK, so now we have the equation y-
3=7-y, but what do we do now?
 Now, we have to make use of the
moving of values to solve the
equation(find the values of x and y)

5. Moving of values
 What I mean by moving of values is
moving a certain value, be it number
or symbol, from one side of the
equation to another.(By one side I
mean the left or right side of the “=“
sign)

6. Changing of signs
 If we want to move values from one
side to another, we have to change
the signs in front of it(+, -,
x(multiplication sign, not the symbol
x), divide)
 However, we cannot change it to
any random sign, but we must
change it to the “opposite” sign.

7. Opposite sign?
 By opposite sign I mean that plus is the
opposite of minus, multiply is the
opposite of divide, etc.
 So if we want to move a +6 value to the
other side, we have to change it to -
6(and vice versa). We do the same thing
for multiplication and divide as well(x6
change to divided by 6 and vice versa)

8. Example
 For example, if 10+2 = 12, 10=12-2
 If 10-2=8, 10=8+2
 If 10x2=20, 10 = 20 divided by 2
 If 10 divided by 2=5, 10=5x2

9. Solving the equation
 Now, back to the equation: y-3=7-y
 Firstly, we move the -3 on the left side to
the right side to become +3.
 And we will get y=7-y+3
 Adding 7 and 3 together gives us y=10-y

10. Solving the equation
 Now we have to move the –y on the right
side to the left side to become +y
 y+y=10
 Note that if you want to find out a
certain value(y, for example), the
symbol y must be on one side and the
numerical value must be on the other
side

11. Solving the equation
 By adding the 2 y’s on the left side
together, we get: 2y=10
 2y is the same as y x2
 So we have to move the x2 over to the
other side as it is a numerical value,
not a symbol

12. Solving the equation
 y x2=10 so y = 10 divided by 2
 10 divided by 2 =5, so y=5
 Then, we substitute the value y=5
back into one of the original
equation(doesn’t matter which one,
you should get the same answer)

13. Solving the equation
 x=y-3. since we know y=5, we can
substitute that in to the equation x=y-3
 Which will give us x=5-3, so x=2(we
can use x=7-y as well, we would still
get the answer x=2)
 So, x=2, y=5

14. Conclusion
 So that’s all about substitution and
moving of values you need to know

15. Summary
 Substitution means substituting of values
into another equation
 Moving of numbers means you have to
change the signs in front of a number
when moving it.
 When solving for a value, make sure the
symbols are on one side of the “=“ sign
and the numbers are on the other.