Question

Table of values x012 ya369 YB 18 13 1/2 9 which of the following systems is a linear equations with the table values represent
Michael's 3x + 3 y = 4 1/2 x + 18 y = 3x + 3 y = -4 and 1/2 x + 18 y equals 3x + 3 y equals 4 and 1/2 x - 18

Answer 1

To determine which system of equations might correspond to the provided table of values, we first need to clarify the table of values you provided (assuming it's meant to show a relationship between \(x\) and \(y\)). You wrote:

- \(x: 0, 1, 2\)
- \(y: a = 3, 6, 9\)
- \(y: b = 18, 13, \frac{1}{2}\)

It seems like the first part corresponds to a linear relationship that's possibly exponential in some entries, but without further clarification, let’s assume the pairs are:

1. \( (0, 3) \)
2. \( (1, 6) \)
3. \( (2, 9) \)

and another set with

1. \( (0, 18) \)
2. \( (1, 13) \)
3. \( (2, \frac{1}{2}) \)

Next, let’s simplify the systems you mentioned.

1. **System 1**:
\[
3x + 3y = 4 \quad \text{(Equation 1)}
\]
\[
\frac{1}{2}x + 18y = 3 \quad \text{(Equation 2)}
\]

2. **System 2**:
\[
3x + 3y = -4 \quad \text{(Equation 3)}
\]
\[
\frac{1}{2}x + 18y = 3 \quad \text{(Equation 4)}
\]

3. **System 3**:
\[
3x + 3y = 4 \quad \text{(Equation 1)}
\]
\[
\frac{1}{2}x - 18 = 3 \quad \text{(Equation 5)}
\]

4. **System 4**:
\[
3x + 3y = \frac{1}{2} \quad \text{(Equation 6)}
\]
\[
\frac{1}{2}x - 18 = 3 \quad \text{(Equation 7)}
\]

Now let’s evaluate these equations with the points.

### Testing System 1:
\[
3(0) + 3(3) = 9 \quad \text{(not 4, hence incorrect)}
\]

### Testing System 2:
\[
3(0) + 3(3) = 9 \quad \text{(not -4, hence incorrect)}
\]

### Testing System 3:
\[
3(0) + 3(3) = 9 \quad \text{(not 4, hence incorrect)}
\]

### Testing System 4:
\[
3(0) + 3(3) = 9 \quad \text{(not 1/2, hence incorrect)}
\]

With further analysis of the other sets involving \(y\) values, you need to clarify how it is being constructed from the context.

This step would help in clarifying which system of equations corresponds to a linear model based on the table values you provided or confirm which points to use from \(a\) or \(b\).

Let me know if this interpretation aligns with your data or clarify any misinterpretation so I can assist further!