To determine whether Susie is correct and if the system of equations has infinitely many solutions, we need to find the equations of the lines given their points.
Line 1 passes through the points (2, -13) and (-2, -1).
- Calculate the slope of Line 1:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1 - (-13)}{-2 - 2} = \frac{12}{-4} = -3 \]
- Use point-slope form \(y - y_1 = m(x - x_1)\) to find the equation of Line 1 using point (2, -13):
\[ y - (-13) = -3(x - 2) \ y + 13 = -3x + 6 \ y = -3x - 7 \]
Line 2 passes through the points (5, -22) and (-3, 2).
- Calculate the slope of Line 2:
\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - (-22)}{-3 - 5} = \frac{24}{-8} = -3 \]
- Use point-slope form \(y - y_1 = m(x - x_1)\) to find the equation of Line 2 using point (5, -22):
\[ y - (-22) = -3(x - 5) \ y + 22 = -3x + 15 \ y = -3x - 7 \]
Both lines have the same slope and the same y-intercept, which means they are actually the same line, not just parallel lines. Hence, they have infinitely many solutions.
Conclusion: Yes, Susie is correct. The answer is:
Yes, Susie is correct.