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:
x 2
And we know that x=6 ...  
... then we can "substitute" 6 for x:
6 2 = 4

 

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 x2 + xy ?

Put "3" where "x" is, and "4" where "y" is:

32 + 3×4 = 3×3 + 12 = 21

Example: If x=3 (but we don't know "y"), then what is x2 + xy ?

Put "3" where "x" is:

32 + 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 + x2 ?

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