Substitution in Algebra
"Substitute" means to put in the place of another.
Substitution
In Algebra "Substitution" means putting numbers where the letters are:
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When we have: | x − 2 |
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And we know that x=6 ... | |
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... then we can substitute 6 for x: | 6 − 2 = 4 |
Example: When x=2, what's 10x + 4 ?
Put "2" where "x" is:
102 + 4 = 5 + 4 = 9
Example: When x=5, what's x + x2 ?
Put "5" where "x" is:
5 + 52 = 5 + 2.5 = 7.5
Example: If x=3 and y=4, then what's 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's x2 + xy ?
Put "3" where "x" is:
32 + 3y = 9 + 3y
(that's 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 we substitute negative numbers, it is best to put () around them so we get the calculations right.
(−2)2 = (−2) × (−2) = +4
Without parentheses, −22 means −(2 × 2) = −4, not +4
Example: If x = −2, then what's 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
due to these special rules:
| Rule | Adding or Subtracting |
Multiplying or Dividing |
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|---|---|---|---|---|
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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 |
1573, 1574, 299, 300, 1575, 1576, 2328, 1577, 2329, 2330