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The point (0,-2) is a solution to which system?
(1 point)
Responses
-4x + y = 6
-5x - y = 21
-4x + y = 6 -5x - y = 21
-5x = y - 3
3x - 8y = 24
-5x = y - 3 3x - 8y = 24
x + y = 2
-x + 2y = 16
x + y = 2 -x + 2y = 16
-5x + y = -2
-3x + 6y = -12
To determine which system the point (0,-2) is a solution to, we can substitute the x and y values of the point into each equation of the systems and see which one gives a true statement.
Let's substitute (0,-2) into the first system:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
The statement is false.
Now let's substitute (0,-2) into the second system:
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21
The statement is false.
Now let's substitute (0,-2) into the third system:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
The statement is false.
Now let's substitute (0,-2) into the fourth system:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
The statement is false.
Now let's substitute (0,-2) into the fifth system:
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24
The statement is false.
Now let's substitute (0,-2) into the sixth system:
(0) + (-2) = 2
-2 = 2
The statement is false.
Now let's substitute (0,-2) into the seventh system:
-(0) + 2(-2) = 16
0 - 4 = 16
-4 = 16
The statement is false.
Finally, let's substitute (0,-2) into the eighth system:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
The statement is true.
Therefore, the point (0,-2) is a solution to the eighth system: -5x + y = -2 and -3x + 6y = -12.
To determine which system the point (0, -2) is a solution to, we can substitute the x and y values of the point into each equation and see which equation is satisfied.
Let's consider each system and substitute (0, -2) into each equation.
System 1: -4x + y = 6 and -5x - y = 21
Substituting (0, -2) into the first equation:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6 (Not satisfied)
Substituting (0, -2) into the second equation:
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21 (Not satisfied)
System 2: -5x = y - 3 and 3x - 8y = 24
Substituting (0, -2) into the first equation:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5 (Not satisfied)
Substituting (0, -2) into the second equation:
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24 (Not satisfied)
System 3: x + y = 2 and -x + 2y = 16
Substituting (0, -2) into the first equation:
0 + (-2) = 2
-2 = 2 (Not satisfied)
Substituting (0, -2) into the second equation:
-0 + 2(-2) = 16
-4 = 16 (Not satisfied)
System 4: -5x + y = -2 and -3x + 6y = -12
Substituting (0, -2) into the first equation:
-5(0) + (-2) = -2
0 - 2 = -2 (Satisfied)
Substituting (0, -2) into the second equation:
-3(0) + 6(-2) = -12
0 - 12 = -12 (Satisfied)
From the calculations, the point (0, -2) is a solution to the system -5x + y = -2 and -3x + 6y = -12.
To determine which system the point (0,-2) is a solution to, we can substitute the coordinates of the point into each equation of the system and check if the equation is satisfied.
1) -4x + y = 6
Substituting (0,-2):
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
2) -5x - y = 21
Substituting (0,-2):
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21
3) -4x + y = 6 and -5x - y = 21
Substituting (0,-2) into both equations:
-4(0) + (-2) = 6
0 - 2 = 6
-2 = 6
-5(0) - (-2) = 21
0 + 2 = 21
2 = 21
4) -5x = y - 3 and 3x - 8y = 24
Substituting (0,-2) into both equations:
-5(0) = (-2) - 3
0 = -2 - 3
0 = -5
3(0) - 8(-2) = 24
0 + 16 = 24
16 = 24
5) x + y = 2 and -x + 2y = 16
Substituting (0,-2) into both equations:
(0) + (-2) = 2
-2 = 2
-(0) + 2(-2) = 16
0 - 4 = 16
-4 = 16
6) -5x + y = -2 and -3x + 6y = -12
Substituting (0,-2) into both equations:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
-3(0) + 6(-2) = -12
0 - 12 = -12
-12 = -12
Based on our calculations, the point (0,-2) is a solution to the system: -4x + y = 6 and -5x - y = 21.