To determine whether Trang is correct about the system of equations having no solution, we can analyze the given equations:
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First equation: \( y = -2(x + 3) \) can be rewritten: \[ y = -2x - 6 \] This has a slope of \(-2\) and a y-intercept of \(-6\).
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Second equation: \( y = -2x + 3 \) has a slope of \(-2\) and a y-intercept of \(3\).
Now we can compare the two equations:
- Both lines have the same slope of \(-2\).
- However, they have different y-intercepts (\(-6\) for the first equation and \(3\) for the second).
Lines that have the same slope but different y-intercepts are parallel and will never intersect, which means they have no solution.
Hence, the correct explanation for Trang's statement is:
A. Trang is correct because the lines have the same slope but different y-intercepts.