Algebra - Substitution
"Substitute" means to put in the place of another.
Substitution
In Algebra "Substitution" means putting numbers where the letters are:
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If you have: |
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And you know that x=6 ... | ||||||
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... then you can "substitute" 6 for x: |
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Example 1: If x=5 then what is 10/x + 4 ?
Put "5" where "x" is:
10/5 + 4 = 2 + 4 = 6
Example 2: 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 3: If x=3 (but you don't know "y"), then what is x2 + xy ?
Put "3" where "x" is:
32 + 3y = 9 + 3y
(that is as far as you can get)
As that last example showed, you 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 4: If x = -2, then what is 1-x+x2 ?
Put "(-2)" where "x" is:
1 - (-2) + (-2)2 = 1 + 2 + 4 = 7
Note: if you don't know why
- the - (-2) became +2 or
- the (-2)2 became +4
then here is a quick summary:
| Rule | Adding or Subtracting | Multiplying or Dividing | |
|---|---|---|---|
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Two like signs become a positive sign | 3+(+2) = 3 + 2 = 5 | 3 × 2 = 6 |
| 6-(-3) = 6 + 3 = 9 | (-3) × (-2) = 6 | ||
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Two unlike signs become a negative sign | 7+(-2) = 7 - 2 = 5 | 3 × (-2) = -6 |
| 8-(+2) = 8 - 2 = 6 | (-3) × 2 = -6 |