To determine which system has the point (0, -2) as a solution, we need to substitute \(x = 0\) and \(y = -2\) into each equation of the given systems and see which one holds true.
System 1:
-
\(x + y = 2\)
- \(0 + (-2) = 2\)
- \(-2 \neq 2\) (Not a solution)
-
\(-x + 2y = 16\)
- \(-0 + 2(-2) = 16\)
- \(-4 \neq 16\) (Not a solution)
So, (0, -2) is not a solution to this system.
System 2:
-
\(-5x = y - 3\)
- \(-5(0) = -2 - 3\)
- \(0 = -5\) (Not a solution)
-
\(3x - 8y = 24\)
- \(3(0) - 8(-2) = 24\)
- \(16 \neq 24\) (Not a solution)
So, (0, -2) is not a solution to this system as well.
System 3:
-
\(-4x + y = 6\)
- \(-4(0) + (-2) = 6\)
- \(-2 \neq 6\) (Not a solution)
-
\(-5x - y = 21\)
- \(-5(0) - (-2) = 21\)
- \(2 \neq 21\) (Not a solution)
So, (0, -2) is not a solution to this system either.
System 4:
-
\(-5x + y = -2\)
- \(-5(0) + (-2) = -2\)
- \(-2 = -2\) (True, it is a solution)
-
\(-3x + 6y = -12\)
- \(-3(0) + 6(-2) = -12\)
- \(-12 = -12\) (True, it is a solution)
(0, -2) is a solution to this system.
Therefore, the correct system is: -5x + y = -2, -3x + 6y = -12.