Susie determined that the system of equations below has infinitely many solutions.
The first line goes through the points (2, -13) and (-2, -1).
The second line goes through the points (5, -22) and (-3, 2). Is she correct?
No, the lines are parallel.
She may or may not be correct as the lines possibly cross.
No, there is no point of intersection.
Yes, Susie is correct.
No, the lines are parallel.
No, Susie is not correct. There is no point of intersection between the two lines.
No, Susie is not correct. The system of equations does not have infinitely many solutions.
To determine if the system of equations has infinitely many solutions or not, we need to check if the lines intersect at a single point or if they are parallel.
We can start by finding the slope of each line. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula:
slope = (y2 - y1) / (x2 - x1)
For the first line passing through (2, -13) and (-2, -1), the slope is:
slope1 = (-1 - (-13)) / (-2 - 2) = 12 / -4 = -3
For the second line passing through (5, -22) and (-3, 2), the slope is:
slope2 = (2 - (-22)) / (-3 - 5) = 24 / -8 = -3
Since both lines have the same slope of -3, they are parallel and will never intersect. Therefore, the system of equations does not have a point of intersection, indicating that Susie is not correct.