The point (0,-2) is a solution to which system?
-4x + y = 6
-5x - y = 21
-5x + y = -2
-3x + 6y = -12
x + y = 2
-x + 2y = 16
-5x = y - 3
3x - 8y = 24
The point (0,-2) is a solution to the system:
-x + 2y = 16
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 to see if they hold true.
Let's start with the first system:
-4x + y = 6
Substituting x = 0 and y = -2:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
Since -2 is not equal to 6, the point (0, -2) is not a solution to the first system.
Moving on to the second system:
-5x + y = -2
Substituting x = 0 and y = -2:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
Since -2 is equal to -2, the point (0, -2) is a solution to the second system.
Now let's check the third system:
x + y = 2
Substituting x = 0 and y = -2:
0 + (-2) = 2
-2 = 2
Since -2 is not equal to 2, the point (0, -2) is not a solution to the third system.
Lastly, the fourth system:
-5x = y - 3
Substituting x = 0 and y = -2:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
Since 0 is not equal to -5, the point (0, -2) is not a solution to the fourth system.
Therefore, the point (0, -2) is a solution to the second system (-5x + y = -2; -3x + 6y = -12).
To check whether the point (0,-2) is a solution to a given system of equations, we substitute the values x = 0 and y = -2 into each equation and see if the equation holds true.
Let's go through each system:
System 1:
-4(0) + (-2) = 6 ---> 0 - 2 = 6 ---> -2 = 6 (Not true)
-5(0) - (-2) = 21 ---> 0 + 2 = 21 ---> 2 = 21 (Not true)
Therefore, (0,-2) is not a solution to System 1.
System 2:
-5(0) + (-2) = -2 ---> 0 - 2 = -2 ---> -2 = -2 (True)
-3(0) + 6(-2) = -12 ---> 0 - 12 = -12 ---> -12 = -12 (True)
Therefore, (0,-2) is a solution to System 2.
System 3:
(0) + (-2) = 2 ---> -2 = 2 (Not true)
-(-2) + 2(-2) = 16 ---> 2 - 4 = 16 ---> -2 = 16 (Not true)
Therefore, (0,-2) is not a solution to System 3.
System 4:
-5(0) = (-2) - 3 ---> 0 = -2 - 3 ---> 0 = -5 (Not true)
3(0) - 8(-2) = 24 ---> 0 + 16 = 24 ---> 16 = 24 (Not true)
Therefore, (0,-2) is not a solution to System 4.
Based on the above analysis, the point (0,-2) is only a solution to System 2:
-5x + y = -2
-3x + 6y = -12.