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.
