susie determined that the system of equations below has infinitely many solutions

Question

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?

yes, susie is correct
she may or may not be correct as the lines possibly cross,
no the lines are arallel
no, there is no point of intersection

Answer 1

To determine if the system of equations has infinitely many solutions, we need to check if the lines are parallel or if they intersect at one point.

We can find the equation of the first line using the two given points. The slope of the line is (change in y / change in x):

m1 = (-1 - (-13)) / (-2 - 2) = 12 / 4 = 3

Using the point-slope formula, the equation of the first line can be found:

y - (-13) = 3(x - 2)
y + 13 = 3x - 6
y = 3x - 19

Similarly, we can find the equation of the second line:

m2 = (2 - (-22)) / (-3 - 5) = 24 / (-8) = -3

Using the point-slope formula, the equation of the second line can be found:

y - (-22) = -3(x - 5)
y + 22 = -3x + 15
y = -3x - 7

Now, we can compare the slopes of the two lines. If the slopes are equal, the lines are parallel, and if they are different, the lines intersect at one point.

Since the slopes of the lines, 3 and -3, are not equal, the lines do not intersect at one point. Therefore, Susie is incorrect in her determination about the system of equations having infinitely many solutions.