The point (0,-2) is a solution to which system?
(1 point)
Responses
-5x + y = -2
-3x + 6y = -12
-5x + y = -2 -3x + 6y = -12
x + y = 2
-x + 2y = 16
x + y = 2 -x + 2y = 16
-5x = y - 3
3x - 8y = 24
-5x = y - 3 3x - 8y = 24
-4x + y = 6
-5x - y = 21
The point (0,-2) is a solution to the system of equations:
-5x + y = -2
-3x + 6y = -12
To determine which system the point (0,-2) is a solution to, substitute the coordinates x=0 and y=-2 into each equation and check if the equality holds.
Let's go through each system:
1. -5x + y = -2:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
The point (0,-2) satisfies the equation.
2. -3x + 6y = -12:
-3(0) + 6(-2) = -12
0 - 12 = -12
-12 = -12
The point (0,-2) satisfies the equation.
3. -5x + y = -2 and -3x + 6y = -12:
Checking both equations with the given coordinates, we have:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
-3(0) + 6(-2) = -12
0 - 12 = -12
-12 = -12
The point (0,-2) satisfies both equations.
4. x + y = 2:
0 + (-2) = 2
-2 = 2
The point (0,-2) does not satisfy the equation.
5. -x + 2y = 16:
-(0) + 2(-2) = 16
-4 = 16
The point (0,-2) does not satisfy the equation.
6. x + y = 2 and -x + 2y = 16:
Checking both equations with the given coordinates, we have:
0 + (-2) = 2
-2 = 2
-(0) + 2(-2) = 16
-4 = 16
The point (0,-2) does not satisfy both equations.
7. -5x = y - 3:
-5(0) = -2 - 3
0 = -5
The point (0,-2) does not satisfy the equation.
8. 3x - 8y = 24:
3(0) - 8(-2) = 24
16 = 24
The point (0,-2) does not satisfy the equation.
9. -5x = y - 3 and 3x - 8y = 24:
Checking both equations with the given coordinates, we have:
-5(0) = -2 - 3
0 = -5
3(0) - 8(-2) = 24
16 = 24
The point (0,-2) does not satisfy both equations.
10. -4x + y = 6:
-4(0) - (-2) = 6
2 = 6
The point (0,-2) does not satisfy the equation.
11. -5x - y = 21:
-5(0) - (-2) = 21
2 = 21
The point (0,-2) does not satisfy the equation.
From the above analysis, the point (0,-2) is a solution to the following systems:
- -5x + y = -2
- -3x + 6y = -12
- -5x + y = -2 and -3x + 6y = -12
To determine whether the point (0, -2) is a solution to a given system of equations, we need to substitute the values of x and y in each equation and check if both sides are equal.
Let's go through each system of equations:
1) -5x + y = -2
Substituting x = 0 and y = -2: (-5 * 0) + (-2) = -2
Simplifying: -2 = -2
The left side is equal to the right side, so (0, -2) is a solution to this system.
2) -3x + 6y = -12
Substituting x = 0 and y = -2: (-3 * 0) + (6 * -2) = -12
Simplifying: -12 = -12
The left side is equal to the right side, so (0, -2) is a solution to this system.
3) -5x + y = -2 and -3x + 6y = -12
Substituting x = 0 and y = -2 in the first equation: (-5 * 0) + (-2) = -2
Simplifying: -2 = -2
The left side is equal to the right side for the first equation.
Substituting x = 0 and y = -2 in the second equation: (-3 * 0) + (6 * -2) = -12
Simplifying: -12 = -12
The left side is equal to the right side for the second equation.
Therefore, (0, -2) is a solution to this system.
4) x + y = 2 and -x + 2y = 16
Substituting x = 0 and y = -2 in the first equation: 0 + (-2) = 2
Simplifying: -2 = 2
The left side is not equal to the right side for the first equation, so (0, -2) is not a solution to this system.
5) -x + 2y = 16 and -5x = y - 3
Substituting x = 0 and y = -2 in the first equation: -(0) + 2(-2) = 16
Simplifying: -4 = 16
The left side is not equal to the right side for the first equation, so (0, -2) is not a solution to this system.
6) -5x = y - 3 and 3x - 8y = 24
Substituting x = 0 and y = -2 in the first equation: -5(0) = (-2) - 3
Simplifying: 0 = -5
The left side is not equal to the right side for the first equation, so (0, -2) is not a solution to this system.
7) -4x + y = 6 and -5x - y = 21
Substituting x = 0 and y = -2 in the first equation: -4(0) + (-2) = 6
Simplifying: -2 = 6
The left side is not equal to the right side for the first equation, so (0, -2) is not a solution to this system.
To summarize, the point (0, -2) is a solution to the following system of equations:
-5x + y = -2
-3x + 6y = -12