To determine which system of linear equations the table of values represents, let's first identify the equations corresponding to the values of \( y_a \) and \( y_b \) at various values of \( x \).
Starting with the first column for \( y_a \):
- For \( x = 0 \), \( y_a = 3 \)
- For \( x = 1 \), \( y_a = 6 \)
- For \( x = 2 \), \( y_a = 9 \)
Let's find the equation for \( y_a \). The slope \( m \) can be defined as \( \frac{change\ in\ y}{change\ in\ x} \):
- From \( (0,3) \) to \( (1,6) \): \( m = \frac{6 - 3}{1 - 0} = \frac{3}{1} = 3 \)
- From \( (1,6) \) to \( (2,9) \): \( m = \frac{9 - 6}{2 - 1} = \frac{3}{1} = 3 \)
Thus, the slope is consistent, and we can establish:
- The point-slope form \( y - 3 = 3(x - 0) \) gives us: \[ y_a = 3x + 3 \]
Now let's analyze the second column for \( y_b \):
- For \( x = 0 \), \( y_b = 18 \)
- For \( x = 1 \), \( y_b = 1312 \)
- For \( x = 2 \), \( y_b = 9 \)
Now, let's find the equation for \( y_b \). The change from \( (0,18) \) to \( (1,1312) \) and the change to \( (2,9) \) seems inconsistent, indicating a miscalculation or misunderstanding.
From our observed trends and calculations, we derived:
- \( y_a = 3x + 3 \)
- \( y_b \) needs to be calculated from more points but appears quadratic or odd due to inconsistencies.
However, as per the options provided, we specifically need \( y_a \) and \( y_b \) in the systems mentioned.
Given these considerations, the first equation \( y_a = 3x + 3 \) correlates best with the options, as we derived from consistent points.
Given the provided options, the correct representation appears to be:
Option: {y = 3x + 3 y = 4 and working out parallel with the last values seen seems \( 12x + 18 \).
Substitutions and additional checks can verify, but the assumption from provided patterns must align with \( y_a \).
Final selections hinge more on double-check values at end given systems.