The point (0,-2) is a solution to which system?
x + y = 2
-x + 2y = 16
-5x = y - 3
3x - 8y = 24
-4x + y = 6
-5x - y = 21
-5x + y = -2
-3x + 6y = -12
The point (0,-2) is a solution to the system:
-3x + 6y = -12
To determine if the point (0, -2) is a solution to each of the given systems, we need to substitute the values of x and y into each equation and see if both equations are satisfied.
System 1:
x + y = 2
Substituting x = 0 and y = -2:
0 + (-2) = 2
-2 = 2 (not satisfied)
-x + 2y = 16
Substituting x = 0 and y = -2:
-0 + 2(-2) = 16
-4 = 16 (not satisfied)
Therefore, the point (0, -2) is not a solution to System 1.
System 2:
-5x = y - 3
Substituting x = 0 and y = -2:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5 (not satisfied)
3x - 8y = 24
Substituting x = 0 and y = -2:
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24 (not satisfied)
Therefore, the point (0, -2) is not a solution to System 2.
System 3:
-4x + y = 6
Substituting x = 0 and y = -2:
-4(0) + (-2) = 6
-2 = 6 (not satisfied)
-5x - y = 21
Substituting x = 0 and y = -2:
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21 (not satisfied)
Therefore, the point (0, -2) is not a solution to System 3.
System 4:
-5x + y = -2
Substituting x = 0 and y = -2:
-5(0) + (-2) = -2
-2 = -2 (satisfied)
-3x + 6y = -12
Substituting x = 0 and y = -2:
-3(0) + 6(-2) = -12
0 + (-12) = -12
-12 = -12 (satisfied)
Therefore, the point (0, -2) is a solution to System 4.
To determine which system the point (0,-2) is a solution to, we can substitute the values of x = 0 and y = -2 into each system and check if the equations are satisfied.
1) x + y = 2:
Substituting the values, 0 + (-2) = 2 which is not true. Therefore, (0,-2) is not a solution to this system.
2) -x + 2y = 16:
Substituting the values, -0 + 2(-2) = 16 which is not true. Therefore, (0,-2) is not a solution to this system.
3) -5x = y - 3:
Substituting the values, -5(0) = (-2) - 3 which is not true. Therefore, (0,-2) is not a solution to this system.
4) 3x - 8y = 24:
Substituting the values, 3(0) - 8(-2) = 24 which is true. Therefore, (0,-2) is a solution to this system.
5) -4x + y = 6:
Substituting the values, -4(0) + (-2) = 6 which is not true. Therefore, (0,-2) is not a solution to this system.
6) -5x - y = 21:
Substituting the values, -5(0) - (-2) = 21 which is not true. Therefore, (0,-2) is not a solution to this system.
Based on the above analysis, the point (0,-2) is a solution to the system 3x - 8y = 24.