Math Skill: Variable Substitution 2
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## Variable Substitution 2

### Prerequisites

Before attempting this topic, it is recommended that you understand the following:
• Addition and subtraction of negative numbers
• Multiplication of negative numbers
• How exponents work
Variable substitution as a concept is very basic. Wherever you see a variable, substitute the value provided and compute the value of the expression. To get the answer quickly, you may find it useful to combine like terms first before doing the substitution.

Example 1:

Evaluate: z + y + z + 2z + 3z
where y=1,z=2.

Solution
Combine and arrange terms: y + 7z

Substitute the values:
1 + 7(2)

Notes
See how we combined the terms first before doing the substitution? If we had not combined terms first, the substitution would look like this:
2 + 1 + 2 + 2(2) + 3(2) =
2 + 1 + 2 + 4 + 6 =
15

Although you would succeed without combining terms, if the numbers had been larger, this would have clearly been more difficult.

Example 2:
Evaluate: 3y 3 + 3z 2 - x + 3y
where x=-3,y=2,z=-3.

Solution
Combine and arrange terms: -x + 3y 3 + 3y + 3z 2

Substitute the values:
-(- 3) + 3(2 3) + 3(2) + 3(( - 3) 2)

3 + 24 + 6 + 27 = 60

Notes
Although it isn't necessary, we reordered the terms first alphabetically, and then by order of magnitude. This is generally a good habit because your teacher might require you to write expressions in this order.

As you can see, substitution involving negative numbers can be tricky. For example, the z2 term evaluates to a positive number even though z=-3.

### Complexity=1, Mode=no-exp

Evaluate.
 1.   Evaluate: 3x + z - 2z + 2z + zwhere x=3,z=2. 2.   Evaluate: - 2x + x - y - 3y - 2ywhere x=5,y=1.

### Complexity=1, Mode=pos-num

Evaluate.
 1.   Evaluate: -y 3 + 2x 3 + y 3 + 2y 3where x=1,y=2. 2.   Evaluate: - 3x 2 - 3z 2 + 2y 3 - 3xwhere x=3,y=1,z=4.

### Complexity=1, Mode=neg-num

Evaluate.
 1.   Evaluate: x + 3y - 2z 3 - 2y 2where x=2,y=-3,z=2. 2.   Evaluate: -x 3 + 3y 3 + 2x 2 - zwhere x=-2,y=-2,z=4.

### Complexity=1, Mode=no-exp

Evaluate.
1Evaluate: 3x + z - 2z + 2z + z
where x=3,z=2.
Solution
Combine and arrange terms: 3x + 2z

Substitute the values:
3(3) + 2(2)

2Evaluate: - 2x + x - y - 3y - 2y
where x=5,y=1.
Solution
Combine and arrange terms: -x - 6y

Substitute the values:
-(5) - 6(1)

### Complexity=1, Mode=pos-num

Evaluate.
1Evaluate: -y 3 + 2x 3 + y 3 + 2y 3
where x=1,y=2.
Solution
Combine and arrange terms: 2x 3 + 2y 3

Substitute the values:
2(1 3) + 2(2 3)

2Evaluate: - 3x 2 - 3z 2 + 2y 3 - 3x
where x=3,y=1,z=4.
Solution
Combine and arrange terms: - 3x 2 - 3x + 2y 3 - 3z 2

Substitute the values:
- 3(3 2) - 3(3) + 2(1 3) - 3(4 2)

### Complexity=1, Mode=neg-num

Evaluate.
1Evaluate: x + 3y - 2z 3 - 2y 2
where x=2,y=-3,z=2.
Solution
Combine and arrange terms: x - 2y 2 + 3y - 2z 3

Substitute the values:
2 - 2(( - 3) 2) + 3(- 3) - 2(2 3)