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:
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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: \[ y_a = 2x \]
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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:
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Option 1: { \( y = 2x \); \( y = 3x + 12 \) }
- \( y = 2x \) matches \( y_a \) but does not match \( y_b \).
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Option 2: { \( y = 2x + 3 \); \( y = 12x \) }
- \( y = 2x + 3 \) does not match \( y_a \), and \( y = 12x \) is not consistent with \( y_b \).
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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.
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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.