Algebra  Substitution
"Substitute" means to put in the place of another.
Substitution
In Algebra "Substitution" means putting numbers where the letters are:
When we have: 


And we know that x=6 ...  
... then we can "substitute" 6 for x: 

Example: When x=2, what is 10/x + 4 ?
Put "2" where "x" is:
10/2 + 4 = 5 + 4 = 9
Example: When x=5, what is x + x/2 ?
Put "5" where "x" is:
5 + 5/2 = 5 + 2.5 = 7.5
Example: If x=3 and y=4, then what is x^{2} + xy ?
Put "3" where "x" is, and "4" where "y" is:
3^{2} + 3×4 = 3×3 + 12 = 21
Example: If x=3 (but we don't know "y"), then what is x^{2} + xy ?
Put "3" where "x" is:
3^{2} + 3y = 9 + 3y
(that is as far as we can get)
As that last example showed, we may not always get a number for an answer, sometimes just a simpler formula.
Negative Numbers
When substituting negative numbers, put () around them so you get the calculations right.
Example: If x = −2, then what is 1 − x + x^{2} ?
Put "(−2)" where "x" is:
1 − (−2) + (−2)^{2} = 1 + 2 + 4 = 7
In that last example:
 the − (−2) became +2
 the (−2)^{2} became +4
because of these special rules:
Rule  Adding or Subtracting 
Multiplying or Dividing 


Two like signs become a positive sign  3+(+2) = 3 + 2 = 5  3 × 2 = 6  
6−(−3) = 6 + 3 = 9  (−3) × (−2) = 6  
Two unlike signs become a negative sign  7+(−2) = 7 − 2 = 5  3 × (−2) = −6  
8−(+2) = 8 − 2 = 6  (−3) × 2 = −6 