The point (0,-2) is a solution to which system?
(1 point)
Responses
-4x + y = 6
-5x - y = 21
-5x + y = -2
-3x + 6y = -12
-5x = y - 3
3x - 8y = 24
x + y = 2
-x + 2y = 16
The point (0,-2) is a solution to the system of equations:
-5x + y = -2
-3x + 6y = -12.
To check if the point (0, -2) is a solution to a system of equations, substitute the values of x and y into each equation and see which one(s) satisfy the equation(s).
Let's check each system of equations:
1. -4x + y = 6
Substitute x = 0 and y = -2:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
The equations do not hold true, so (0, -2) is not a solution to this system.
2. -5x + y = -2
Substitute x = 0 and y = -2:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
The equations hold true, so (0, -2) is a solution to this system.
3. -5x = y - 3
Substitute x = 0 and y = -2:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
The equations do not hold true, so (0, -2) is not a solution to this system.
4. x + y = 2
Substitute x = 0 and y = -2:
(0) + (-2) = 2
-2 = 2
The equations do not hold true, so (0, -2) is not a solution to this system.
Therefore, the point (0, -2) is only a solution to the system -5x + y = -2.
To determine which system the point (0, -2) is a solution to, we need to substitute the values of x and y into each equation and see if they satisfy the equations.
Let's start with the first system:
-4x + y = 6 -- (1)
-5x - y = 21 -- (2)
Substituting x = 0 and y = -2 into equation (1):
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
The result is not true, so (0, -2) is not a solution to the first system.
Now let's try the second system:
-5x + y = -2 -- (3)
-3x + 6y = -12 -- (4)
Substituting x = 0 and y = -2 into equation (3):
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
The result is true, so (0, -2) is a solution to the second system.
Therefore, the point (0, -2) is a solution to the system:
-5x + y = -2
-3x + 6y = -12