Which of the following systems of equations has the solution (-2, 1)?
This question requires you to show your work.
(1 point)
Responses
2x−y=−5
and x+2y=10
2 x minus y is equal to negative 5 and x plus 2 y is equal to 10
x−4y=8
and 3x+10=−2y
x minus 4 y is equal to 8 and 3 x plus 10 is equal to negative 2 y
y=−32x−2
and 2x−y=−5
y is equal to negative 3 over 2 x minus 2 and 2 x minus y is equal to negative 5
y=−2x−2
and 2x−2y=5
To find which system of equations has the solution (-2, 1), we substitute x = -2 and y = 1 into each equation and see if both equations hold true.
1. For the system 2x−y=−5 and x+2y=10:
Substitute x = -2 and y = 1 into the first equation:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (True)
Substitute x = -2 and y = 1 into the second equation:
-2 + 2(1) = 10
-2 + 2 = 10
0 = 10 (False)
Therefore, this system of equations does not work.
2. For the system x−4y=8 and 3x+10=−2y:
Substituting x = -2 and y = 1 into the first equation gives:
-2 - 4(1) = 8
-2 - 4 = 8
-6 = 8 (False)
Substituting x = -2 and y = 1 into the second equation gives:
3(-2) + 10 = -2(1)
-6 + 10 = -2
4 = -2 (False)
Therefore, this system of equations does not work.
3. For the system y=−3/2x−2 and 2x−y=−5:
Substituting x = -2 and y = 1 into the first equation gives:
1 = -3/2(-2) - 2
1 = 3 + 2
1 = 5 (False)
Substituting x = -2 and y = 1 into the second equation gives:
2(-2) - 1 = -5
-4 - 1 = -5
-5 = -5 (True)
Therefore, this system of equations does not work.
4. For the system y=−2x−2 and 2x−2y=5:
Substituting x = -2 and y = 1 into the first equation gives:
1 = -2(-2) - 2
1 = 4 - 2
1 = 2 (False)
Substituting x = -2 and y = 1 into the second equation gives:
2(-2) - 2(1) = 5
-4 - 2 = 5
-6 = 5 (False)
Therefore, this system of equations does not work.
None of the given systems of equations have the solution (-2, 1).