To analyze the system of equations provided:
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Equation 1: \(2x - 5 = 6y\) can be rearranged into slope-intercept form (\(y = mx + b\)): \[ 6y = 2x - 5 \] \[ y = \frac{1}{3}x - \frac{5}{6} \]
This line has a slope of \(\frac{1}{3}\) and a y-intercept of \(-\frac{5}{6}\).
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Equation 2: \(y = 13x + 4\) is already in slope-intercept form. It has a slope of \(13\) and a y-intercept of \(4\).
Since the slopes of the two lines are different (\(\frac{1}{3}\) ≠ \(13\)), the lines are not parallel. They will intersect at exactly one point.
Now, analyzing Mya and Liliana's claims:
- Mya says there is no solution, which would be true only if the lines were parallel (which they are not).
- Liliana says there are an infinite number of solutions, which would be true only if the lines were the same line (which they are not).
- The statement that the solution to the system is \((0,4)\) is incorrect; this point lies on \(y = 13x + 4\) but not on the other line.
Considering the accurate analysis of their claims, the option that best explains what is going on is:
Option #1: Only Mya is correct. Two parallel lines do not intersect in any of the points.
However, we should note that this is technically incorrect in the context of these lines and the analysis shows that both Mya and Liliana are wrong regarding the nature of the solutions. Nevertheless, none of the other options accurately convey the nature of the relationship between the two lines based on the equations given.
Thus, the best choice considering the options is Option #1, but remember it does not accurately reflect the reality, as the lines do intersect at one point.
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