The point (0,-2) is a solution to which system? (1 point) Responses -4x + y = 6 -5x - y = 21 -4x + y = 6 -5x - y = 21 -5x = y - 3 3x - 8y = 24 -5x = y - 3 3x - 8y = 24 -5x + y = -2 -3x + 6y = -12 -5x + y = -2 -3x + 6y = -12 x + y = 2 -x + 2y = 16 x + y = 2 -x + 2y = 16
To determine which system the point (0,-2) is a solution to, we can substitute the values of x and y into each equation and see which equations are satisfied.
Let's test the first system of equations:
-4x + y = 6
Substituting x=0 and y=-2:
-4(0) + (-2) = 6
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)
The first system of equations is not satisfied by the point (0,-2).
Now let's test the second system of equations:
-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)
The second system of equations is also not satisfied by the point (0,-2).
Finally, let's test the third system of equations:
-5x + y = -2
Substituting x=0 and y=-2:
-5(0) + (-2) = -2
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)
The point (0,-2) is a solution to the third system of equations:
-5x + y = -2
-3x + 6y = -12
To determine whether the point (0, -2) is a solution to the given system of equations, we will substitute the x and y coordinates of the point into each equation and check if it satisfies them.
Let's start by substituting the point (0, -2) into the first equation:
-4x + y = 6
Substituting x = 0 and y = -2:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
Since -2 does not equal 6, the first equation is not satisfied by the point (0, -2).
Now let's substitute the point into the second equation:
-5x - y = 21
Substituting x = 0 and y = -2:
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21
Since 2 does not equal 21, the second equation is not satisfied by the point (0, -2).
Moving on to the third equation:
-5x = y - 3
Substituting x = 0 and y = -2:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
Since 0 does not equal -5, the third equation is not satisfied by the point (0, -2).
Lastly, let's substitute the point into the fourth equation:
3x - 8y = 24
Substituting x = 0 and y = -2:
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24
Since 16 does not equal 24, the fourth equation is not satisfied by the point (0, -2).
Therefore, the point (0, -2) is not a solution to any of the given systems.
None of the provided options is the correct system for the point (0, -2).