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

.(1 point)
Responses

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

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

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

(0,−2)

1 answer

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

  1. For the pair \( (1, 1) \): \[ 3(1) - 8 = -4(1) \] \[ 3 - 8 = -4 \] \[ -5 \neq -4 \quad (\text{Not a solution}) \]

  2. For the pair \( (0, 2) \): \[ 3(0) - 8 = -4(2) \] \[ -8 = -8 \quad (\text{This is a solution}) \]

  3. For the pair \( (-1, 1) \): \[ 3(-1) - 8 = -4(1) \] \[ -3 - 8 = -4 \] \[ -11 \neq -4 \quad (\text{Not a solution}) \]

  4. For the pair \( (0, -2) \): \[ 3(0) - 8 = -4(-2) \] \[ -8 = 8 \quad (\text{Not a solution}) \]

After checking all ordered pairs, we find that the only solution is:

(0, 2).