Equations in Two Variables Quick Check

Question

1 of 51 of 5 Items
Question
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 2 right parenthesis

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

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

Answer 1

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

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

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

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

4. For \((0, -2)\): \[ 3(0) - 8 = -4(-2) \implies 0 - 8 = 8 \implies -8 \neq 8 \quad \text{(not a solution)} \]

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