The point (0, - 2) is a solution to which system?
(1 point)
A. - 5x + y = - 2
- 3x + 6y = - 12
B. - 5x = y - 3
3x - 8y = 24
C. x + y = 2
- x + 2y = 16
D. - 4x + y = 6
- 5x - y = 21
The point (0, - 2) is a solution to system A.
To determine which system the point (0, -2) is a solution to, we can substitute the values of x and y into each equation of the system and check if the equations are satisfied.
A. -5x + y = -2
Substituting x = 0 and y = -2:
-5(0) + (-2) = -2
0 - 2 = -2
-2 = -2
This equation is satisfied.
-3x + 6y = -12
Substituting x = 0 and y = -2:
-3(0) + 6(-2) = -12
0 - 12 = -12
-12 = -12
This equation is also satisfied.
Since both equations of system A are satisfied when x = 0 and y = -2, the point (0, -2) is a solution to system A.
So the answer is A. -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 system and check which ones satisfy the equations.
Let's go through each system and substitute the x and y values:
A. -5x + y = -2 => -5(0) + (-2) = -2 => 0 - 2 = -2 => -2 = -2
-3x + 6y = -12 => -3(0) + 6(-2) = -12 => 0 - 12 = -12 => -12 = -12
B. -5x = y - 3 => -5(0) = (-2) - 3 => 0 = -5 => Not equal
3x - 8y = 24 => 3(0) - 8(-2) = 24 => 0 + 16 = 24 => 16 = 24
C. x + y = 2 => 0 + (-2) = 2 => -2 = 2 => Not equal
-x + 2y = 16 => -(0) + 2(-2) = 16 => 0 - 4 = 16 => -4 = 16
D. -4x + y = 6 => -4(0) + (-2) = 6 => 0 - 2 = 6 => -2 = 6
-5x - y = 21 => -5(0) - (-2) = 21 => 0 + 2 = 21 => 2 = 21
By substituting the values (0, -2) into each system, we see that only systems A and D satisfy the equations. Therefore, the point (0, -2) is a solution to systems A and D.