To analyze the system of equations given by Mya and Liliana, we need to look at the equations:
- \(2x - 5 = 6y\)
- \(y = 13x + 4\)
First, let's rewrite the first equation in slope-intercept form (y = mx + b):
Starting with:
\[ 2x - 5 = 6y \] Rearranging gives:
\[ 6y = 2x - 5 \quad \Rightarrow \quad y = \frac{1}{3}x - \frac{5}{6} \]
Now we have both equations in the y = mx + b form:
- \(y = \frac{1}{3}x - \frac{5}{6}\) (the line associated with Mya)
- \(y = 13x + 4\) (the line associated with Liliana)
Next, we need to analyze the slopes:
- The slope of the first equation is \(\frac{1}{3}\).
- The slope of the second equation is \(13\).
Since the slopes are different, the lines will intersect at exactly one point, meaning there is one unique solution for this system of equations.
Given this analysis, let's evaluate the options:
- Option #1: Only Mya is correct. Two parallel lines do not intersect in any of the points. (Incorrect, lines are not parallel).
- Option #2: Only Liliana is correct. Because the two equations are parallel, there are an infinite number of solutions. (Incorrect, lines are not parallel).
- Option #3: They are both wrong. The solution to the system of equations is (0,4). (Incorrect, as we haven't calculated the point of intersection).
- Option #4: Only Mya is correct because both equations intersect the y-axis. (Incorrect reasoning, but true that they intersect at one point).
None of the choices accurately describes the situation, so it seems all options provided are incorrect.
However, the one that comes closest is Option #1, but for the reasons mentioned, it is still not correct in the context of the solution provided. The most accurate statement is that there is exactly one solution, which is not captured in any of the provided options.
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