To determine if the system of equations has infinitely many solutions, you need to check if the two lines are equivalent. This occurs when they have the same slope and y-intercept.
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Find the slope of the first line (going through (2, -13) and (-2, -1)): \[ m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-13)}{-2 - 2} = \frac{12}{-4} = -3 \]
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Find the y-intercept (using the point-slope form): Using the point (2, -13): \[ y - (-13) = -3(x - 2) \quad \Rightarrow \quad y + 13 = -3x + 6 \quad \Rightarrow \quad y = -3x - 7 \] So, the equation of the first line is \(y = -3x - 7\).
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Find the slope of the second line (going through (5, -22) and (-3, 2)): \[ m_2 = \frac{2 - (-22)}{-3 - 5} = \frac{24}{-8} = -3 \]
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Find the y-intercept (using the point-slope form): Using the point (5, -22): \[ y - (-22) = -3(x - 5) \quad \Rightarrow \quad y + 22 = -3x + 15 \quad \Rightarrow \quad y = -3x - 7 \] So, the equation of the second line is also \(y = -3x - 7\).
Since both lines have the same slope (-3) and the same y-intercept (-7), they are identical. This means they overlap entirely and thus have infinitely many solutions.
Conclusively, the correct response is:
Yes, Susie is correct.