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)
Yes, Susie is correct.
Yes, Susie is correct.
No, there is one point of intersection
No, there is one point of intersection
No, the lines are parallel
No, the lines are parallel
She may or may not be correct as the lines possibly cross
She may or may not be correct as the lines possibly cross
11 answers
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what does . mean
I apologize for the confusion. It seems there was an error in the response. The correct response is:
She may or may not be correct as the lines possibly intersect.
She may or may not be correct as the lines possibly intersect.
are you sure? cause one answer that i checked was that she is correct so which one is it really
I apologize for the mistake. The correct response is:
Yes, Susie is correct.
Yes, Susie is correct.
so is this the finally answer
Yes, the final answer is:
Yes, Susie is correct.
Yes, Susie is correct.
one more question? how will we work this out
To show that the system of equations has infinitely many solutions, we need to write out the equations of the lines passing through the given points and then show that they are equivalent.
The first line passing through the points (2, -13) and (-2, -1) can be found using the point-slope form:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using (2, -13) and (-2, -1) as the points:
m = (-1 - (-13))/(-2 - 2) = 12/-4 = -3
Using (2, -13):
y - (-13) = -3(x - 2)
y + 13 = -3x + 6
y = -3x - 7
The second line passing through the points (5, -22) and (-3, 2) can be found similarly:
m = (2 - (-22))/(-3 - 5) = 24/-8 = -3
Using (5, -22):
y - (-22) = -3(x - 5)
y + 22 = -3x + 15
y = -3x - 7
Both equations simplify to y = -3x - 7, showing that the lines are equivalent. Therefore, the system has infinitely many solutions.
The first line passing through the points (2, -13) and (-2, -1) can be found using the point-slope form:
y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
Using (2, -13) and (-2, -1) as the points:
m = (-1 - (-13))/(-2 - 2) = 12/-4 = -3
Using (2, -13):
y - (-13) = -3(x - 2)
y + 13 = -3x + 6
y = -3x - 7
The second line passing through the points (5, -22) and (-3, 2) can be found similarly:
m = (2 - (-22))/(-3 - 5) = 24/-8 = -3
Using (5, -22):
y - (-22) = -3(x - 5)
y + 22 = -3x + 15
y = -3x - 7
Both equations simplify to y = -3x - 7, showing that the lines are equivalent. Therefore, the system has infinitely many solutions.
ok thanks
You're welcome! If you have any more questions or need further assistance, feel free to ask. Have a great day!