The point (0,-2) is a solution to which system?
(1 point)
Responses
x + y = 2
-x + 2y = 16
x + y = 2 -x + 2y = 16
-5x = y - 3
3x - 8y = 24
-5x = y - 3 3x - 8y = 24
-5x + y = -2
-3x + 6y = -12
-5x + y = -2 -3x + 6y = -12
-4x + y = 6
-5x - y = 21
The point (0,-2) is a solution to the equation:
x + y = 2
To determine which system contains the point (0, -2) as a solution, you need to substitute the values x = 0 and y = -2 into each system's equations and see which one satisfies both equations.
Let's substitute the values into the first system:
x + y = 2
0 + (-2) = 2
-2 = 2
Since -2 does not equal 2, the first system does not contain the point (0, -2) as a solution.
Now let's substitute the values into the second system:
-x + 2y = 16
-(0) + 2(-2) = 16
0 - 4 = 16
-4 = 16
Again, -4 does not equal 16, so the second system does not contain the point (0, -2) as a solution.
We continue this process for each system, substituting x = 0 and y = -2 into each equation. If we find a system that satisfies both equations, then it contains the point (0, -2) as a solution.
By substituting x = 0 and y = -2 into each equation of the fifth system, we get:
-5x = y - 3
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
Since 0 does not equal -5, the fifth system does not contain the point (0, -2) as a solution.
Finally, let's substitute the values into the last system:
-4x + y = 6
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
Again, -2 does not equal 6, so the last system does not contain the point (0, -2) as a solution.
After checking all the systems, none of them contain the point (0, -2) as a solution.
To determine which system the point (0,-2) is a solution to, we need to substitute the values of x = 0 and y = -2 into each equation and check if the equations are satisfied.
1) x + y = 2:
Plugging in x = 0 and y = -2, we get:
0 + (-2) = 2
-2 = 2
This equation is not satisfied, so (0,-2) is not a solution to this system.
2) -x + 2y = 16:
Plugging in x = 0 and y = -2, we get:
-(0) + 2(-2) = 16
-4 = 16
This equation is not satisfied, so (0,-2) is not a solution to this system.
3) -5x = y - 3
Plugging in x = 0 and y = -2, we get:
-5(0) = (-2) - 3
0 = -5
This equation is not satisfied, so (0,-2) is not a solution to this system.
4) 3x - 8y = 24
Plugging in x = 0 and y = -2, we get:
3(0) - 8(-2) = 24
16 = 24
This equation is not satisfied, so (0,-2) is not a solution to this system.
5) -5x + y = -2
Plugging in x = 0 and y = -2, we get:
-5(0) + (-2) = -2
-2 = -2
This equation is satisfied, so (0,-2) is a solution to this system.
6) -3x + 6y = -12
Plugging in x = 0 and y = -2, we get:
-3(0) + 6(-2) = -12
-12 = -12
This equation is satisfied, so (0,-2) is a solution to this system.
Therefore, the point (0,-2) is a solution to the system of equations:
-5x + y = -2
-3x + 6y = -12