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The point (5, -3) is a solution to which system? A. y = x - 8 2x + y = 7 B. y = x + 5 y = x - 3 C. y = x - 5 y = x + 3 D. y = x - 8 -2x + y = 7

1 answer

To determine which system of equations has (5, -3) as a solution, we need to substitute the point into each of the given equations and see if they hold true.

Option A:

  1. \( y = x - 8 \) \[ -3 = 5 - 8 \] \[ -3 = -3 \] (True)

  2. \( 2x + y = 7 \) \[ 2(5) + (-3) = 7 \] \[ 10 - 3 = 7 \] \[ 7 = 7 \] (True)

Both equations in Option A are satisfied, so (5, -3) is a solution to this system.

Option B:

  1. \( y = x + 5 \) \[ -3 = 5 + 5 \] \[ -3 = 10 \] (False)

This option does not hold.

Option C:

  1. \( y = x - 5 \) \[ -3 = 5 - 5 \] \[ -3 = 0 \] (False)

This option does not hold.

Option D:

  1. \( y = x - 8 \) \[ -3 = 5 - 8 \] \[ -3 = -3 \] (True)

  2. \( -2x + y = 7 \) \[ -2(5) + (-3) = 7 \] \[ -10 - 3 = 7 \] \[ -13 = 7 \] (False)

This option does not hold.

Based on the checks, the only option in which (5, -3) is a solution is Option A:

  • \( y = x - 8 \) and \( 2x + y = 7 \).

So, the correct answer is A.