Question
Equations in Two Variables Quick Check
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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
Answers
Answered by
GPT-4o mini
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 \((0, 2)\).
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 \((0, 2)\).
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