Question

Use the table to answer the question.

Table of Values

x ya yb
0 0 3
1 2 3.5
2 4 4
Which of the following systems of linear equations does the table of values represent?

(1 point)
Responses

{y=2xy=3x+12


{y=2x+3y=12x


{y=12xy=2x+3


{y=2xy=12x+3

Answer 1

To determine which system of linear equations the table of values represents, we need to analyze the given values for \( y_a \) and \( y_b \) separately and check if they align with any of the provided equations.

From the table of values:

1. For \( y_a \):
- When \( x = 0 \), \( y_a = 0 \)
- When \( x = 1 \), \( y_a = 2 \)
- When \( x = 2 \), \( y_a = 4 \)

This indicates that \( y_a \) is a linear function of \( x \) which can be expressed as:
\[
y_a = 2x
\]

2. For \( y_b \):
- When \( x = 0 \), \( y_b = 3 \)
- When \( x = 1 \), \( y_b = 3.5 \)
- When \( x = 2 \), \( y_b = 4 \)

This data suggests a linear relation which can be expressed as:
\[
y_b = 3 + 0.5x
\]

Now, let's analyze the provided options for consistency with these equations:

1. **Option 1**: { \( y = 2x \); \( y = 3x + 12 \) }
- \( y = 2x \) matches \( y_a \) but does not match \( y_b \).

2. **Option 2**: { \( y = 2x + 3 \); \( y = 12x \) }
- \( y = 2x + 3 \) does not match \( y_a \), and \( y = 12x \) is not consistent with \( y_b \).

3. **Option 3**: { \( y = 12x \); \( y = 2x + 3 \) }
- \( y = 2x + 3 \) corresponds to a shifted version of \( y_b \), but does not match. \( y = 12x \) does not match \( y_a \) either.

4. **Option 4**: { \( y = 2x \); \( y = 12x + 3 \) }
- This has \( y = 2x \) which matches \( y_a \), but \( y = 12x + 3 \) does not match \( y_b \).

None of the options directly correspond to the values from the table as derived functions.

However, if we need to choose the best matching system based on \( y_a = 2x \) matching in one of the options, **Option 1** is the best fit as one equation aligns with the linear function in the table \( y = 2x \) for \( y_a \).

Thus, the response would be:
**{y=2x; y=3x+12}**

If you meant combinations or adaptations or meant to investigate other formats within the boundaries of common understanding for a linear system or if there are adjustments or translations needed, please provide that context for different exploration.