Sure, let's break it down step-by-step:
### 1. Determine the variable(s) in each of the following equations:
#### a. [tex]\( 3x + 7y = 4 \)[/tex]
In this equation, we have two terms involving variables: [tex]\( 3x \)[/tex] and [tex]\( 7y \)[/tex]. Hence, the variables are:
- [tex]\( x \)[/tex]
- [tex]\( y \)[/tex]
#### b. [tex]\( -4a + b = -11 \)[/tex]
This equation includes the terms [tex]\( -4a \)[/tex] and [tex]\( b \)[/tex], which involve variables:
- [tex]\( a \)[/tex]
- [tex]\( b \)[/tex]
#### c. [tex]\( 5 \)[/tex]
This equation is a constant value and involves no variables:
- No variables
#### d. [tex]\( 5 + 5 = -3 \)[/tex]
This is simply a numerical statement with no variables present:
- No variables
#### e. [tex]\( -4x^2 - 4x - 4 = 0 \)[/tex]
Here, the equation involves the term [tex]\( x^2 \)[/tex] and [tex]\( x \)[/tex], indicating the variable:
- [tex]\( x \)[/tex]
### Summary of Variables:
1. [tex]\( 3x + 7y = 4 \)[/tex]: Variables are [tex]\( x, y \)[/tex]
2. [tex]\( -4a + b = -11 \)[/tex]: Variables are [tex]\( a, b \)[/tex]
3. [tex]\( 5 \)[/tex]: No variables
4. [tex]\( 5 + 5 = -3 \)[/tex]: No variables
5. [tex]\( -4x^2 - 4x - 4 = 0 \)[/tex]: Variable is [tex]\( x \)[/tex]
### 2. Determine the constant term in each of the following equations:
#### a. [tex]\( y = -2x + 7 \)[/tex]
In the equation [tex]\( y = -2x + 7 \)[/tex], the constant term is the value that does not involve variables:
- Constant term: [tex]\( 7 \)[/tex]
#### b. [tex]\( y = x^3 + 5x - 18 \)[/tex]
In this one, the constant term is the value [tex]\( -18 \)[/tex], as it does not change with [tex]\( x \)[/tex]:
- Constant term: [tex]\( -18 \)[/tex]
#### f. [tex]\( 2 \)[/tex]
This entire equation is a constant term itself:
- Constant term: [tex]\( 2 \)[/tex]
#### d. [tex]\( 4y - 3s = -8h \)[/tex]
This equation does not have a term that is independent of the variables:
- No constant term: None
#### e. [tex]\( 4b - 8 = 3y \)[/tex]
Finally, the equation [tex]\( 4b - 8 = 3y \)[/tex] has a constant term [tex]\( -8 \)[/tex] on the left-hand side:
- Constant term: [tex]\( -8 \)[/tex]
### Summary of Constant Terms:
1. [tex]\( y = -2x + 7 \)[/tex]: Constant term is [tex]\( 7 \)[/tex]
2. [tex]\( y = x^3 + 5x - 18 \)[/tex]: Constant term is [tex]\( -18 \)[/tex]
3. [tex]\( 2 \)[/tex]: Constant term is [tex]\( 2 \)[/tex]
4. [tex]\( 4y - 3s = -8h \)[/tex]: No constant term
5. [tex]\( 4b - 8 = 3y \)[/tex]: Constant term is [tex]\( -8 \)[/tex]
So the complete solution for the given problems is:
- Variables: [tex]\((x, y), (a, b), (), (), (x,)\)[/tex]
- Constants: [tex]\(7, -18, 2, None, -8\)[/tex]
So, the final answer is:
```
(('x', 'y'), ('a', 'b'), (), (), ('x',), 7, -18, 2, None, -8)
```
