The point (0, - 2) is a solution to which system?
(1 point)
- 5x + y = - 2
- 3x + 6y = - 12
- 5x = y - 3
3x - 8y = 24
x + y = 2
- x + 2y = 16
- 4x + y = 6
- 5x - y = 21
The point (0, -2) is a solution to the system of equations:
- 5x + y = -2
This equation is satisfied when x = 0 and 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 check if it satisfies the equation.
Let's substitute the values x = 0 and y = -2 into each equation:
1) -5x + y = -2
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
2) -3x + 6y = -12
-3(0) + 6(-2) = -12
0 - 12 = -12
-12 = -12
3) -5x = y - 3
-5(0) = (-2) - 3
0 = -5
4) 3x - 8y = 24
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24
5) x + y = 2
0 + (-2) = 2
-2 = 2
6) -x + 2y = 16
-(0) + 2(-2) = 16
0 - 4 = 16
-4 = 16
7) -4x + y = 6
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
8) -5x - y = 21
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21
From the calculations above, we can see that only equations 1) and 2) are satisfied by the values x = 0 and y = -2. Hence, the point (0, -2) is a solution to the system:
-5x + y = -2
-3x + 6y = -12
To find out which system the point (0, -2) is a solution to, we need to substitute the values of x and y in each equation and check if the equation is satisfied with those values.
Let's check each system one by one:
1. -5x + y = -2
Substituting x = 0 and y = -2:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
The equation is satisfied, so (0, -2) is a solution to this system.
2. -3x + 6y = -12
Substituting x = 0 and y = -2:
-3(0) + 6(-2) = -12
0 - 12 = -12
-12 = -12
The equation is satisfied, so (0, -2) is a solution to this system.
3. -5x = y - 3
Substituting x = 0 and y = -2:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
The equation is not satisfied, so (0, -2) is not a solution to this system.
4. 3x - 8y = 24
Substituting x = 0 and y = -2:
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24
The equation is not satisfied, so (0, -2) is not a solution to this system.
5. x + y = 2
Substituting x = 0 and y = -2:
0 + (-2) = 2
-2 = 2
The equation is not satisfied, so (0, -2) is not a solution to this system.
6. -x + 2y = 16
Substituting x = 0 and y = -2:
-(0) + 2(-2) = 16
0 - 4 = 16
-4 = 16
The equation is not satisfied, so (0, -2) is not a solution to this system.
7. -4x + y = 6
Substituting x = 0 and y = -2:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
The equation is not satisfied, so (0, -2) is not a solution to this system.
8. -5x - y = 21
Substituting x = 0 and y = -2:
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21
The equation is not satisfied, so (0, -2) is not a solution to this system.
Therefore, the point (0, -2) is a solution to the first two systems:
-5x + y = -2
and
-3x + 6y = -12.