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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 = -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
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1 answer

To determine which system the point (0, -2) is a solution to, we need to check each equation in the given systems by substituting x = 0 and y = -2.

  1. For the first system:

    • Equation 1: \(-4x + y = 6\)
      • Substitute: \(-4(0) + (-2) = 6 \rightarrow -2 \neq 6\) (not a solution)
    • Equation 2: \(-5x - y = 21\)
      • Substitute: \(-5(0) - (-2) = 21 \rightarrow 2 \neq 21\) (not a solution)

  2. For the second system:

    • Equation 1: \(-4x + y = 6\)
      • We already found it not to be a solution.
    • Equation 2: \(-5x + y = -2\)
      • Substitute: \(-5(0) + (-2) = -2 \rightarrow -2 = -2\) (is a solution)

  3. For the third system:

    • Equation 1: \(-3x + 6y = -12\)
      • Substitute: \(-3(0) + 6(-2) = -12 \rightarrow -12 = -12\) (is a solution)
    • Equation 2: \(-5x + y = -2\)
      • We already found this to be true.

  4. For the fourth system:

    • Equation 1: \(x + y = 2\)
      • Substitute: \(0 + (-2) = 2 \rightarrow -2 \neq 2\) (not a solution)
    • Equation 2: \(-x + 2y = 16\)
      • Substitute: \(-0 + 2(-2) = 16 \rightarrow -4 \neq 16\) (not a solution)

  5. For the fifth system:

    • Equation 1: \(-5x = y - 3\)
      • Substitute: \(-5(0) = -2 - 3 \rightarrow 0 \neq -5\) (not a solution)
    • Equation 2: \(3x - 8y = 24\)
      • Substitute: \(3(0) - 8(-2) = 24 \rightarrow 16 \neq 24\) (not a solution)

Conclusion: Both equations in the second system \(-5x + y = -2\) and \(-3x + 6y = -12\) are true for the point (0, -2). Therefore, the point (0, -2) is a solution to the system:

\(-5x + y = -2\)

\(-3x + 6y = -12\)