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Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y.(1 point)

Responses

(−1,1)
left parenthesis negative 1 comma 1 right parenthesis

(0,−2)
left parenthesis 0 comma negative 2 right parenthesis

(1,1)
left parenthesis 1 comma 1 right parenthesis

(0,2)

1 answer

To determine which ordered pair is a solution to the equation \(3x - 8 = -4y\), we can substitute each pair into the equation and see if both sides are equal.

  1. For the pair \((-1, 1)\): \[ x = -1, \quad y = 1 \] Substitute into the equation: \[ 3(-1) - 8 = -4(1) \ -3 - 8 = -4 \ -11 \neq -4 \quad \text{(not a solution)} \]

  2. For the pair \((0, -2)\): \[ x = 0, \quad y = -2 \] Substitute into the equation: \[ 3(0) - 8 = -4(-2) \ 0 - 8 = 8 \ -8 \neq 8 \quad \text{(not a solution)} \]

  3. For the pair \((1, 1)\): \[ x = 1, \quad y = 1 \] Substitute into the equation: \[ 3(1) - 8 = -4(1) \ 3 - 8 = -4 \ -5 \neq -4 \quad \text{(not a solution)} \]

  4. For the pair \((0, 2)\): \[ x = 0, \quad y = 2 \] Substitute into the equation: \[ 3(0) - 8 = -4(2) \ 0 - 8 = -8 \ -8 = -8 \quad \text{(this is a solution)} \]

The only ordered pair that is a solution to the equation \(3x - 8 = -4y\) is \((0, 2)\).