Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y

Question

.(1 point)
Responses

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

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

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

(0,−2)

Answer 1

To determine which ordered pair is a solution to the equation \(3x - 8 = -4y\), we can substitute the values of \(x\) and \(y\) from each ordered pair into the equation and see if it holds true.

1. For (0, 2): \[ x = 0,\ y = 2 \ 3(0) - 8 = -4(2) \ -8 = -8 \quad \text{(True)} \]

2. For (1, 1): \[ x = 1,\ y = 1 \ 3(1) - 8 = -4(1) \ 3 - 8 = -4 \ -5 = -4 \quad \text{(False)} \]

3. For (−1, 1): \[ x = -1,\ y = 1 \ 3(-1) - 8 = -4(1) \ -3 - 8 = -4 \ -11 = -4 \quad \text{(False)} \]

4. For (0, -2): \[ x = 0,\ y = -2 \ 3(0) - 8 = -4(-2) \ -8 = 8 \quad \text{(False)} \]

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

Answer: (0, 2)