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Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y.(1 point) Responses (0,2) left parenthesi...Asked by Finally Some Answers
Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y .(1 point) Responses (0,−2) left parenthesis 0 comma negative 2 right parenthesis (−1,1) left parenthesis negative 1 comma 1 right parenthesis (1,1) left parenthesis 1 comma 1 right parenthesis (0,2)
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The math teacher asked his students to determine a solution for 1.5x−2y=8 . Which solution below is the correct one?(1 point) Responses Mary believes (4,−7) is a solution. Mary believes left parenthesis 4 comma negative 7 right parenthesis is a solution. Sam believes (−4,−7) is a solution. Sam believes left parenthesis negative 4 comma negative 7 right parenthesis is a solution. Fiona believes (4,7) is a solution. Fiona believes left parenthesis 4 comma 7 right parenthesis is a solution. Peter believes (−4,7) is a solution.
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Select the option below that correctly shows which of the following ordered pairs is part of the solution set for the equation y=4x+2 .(1 point) Responses (3,45) left parenthesis 3 comma 45 right parenthesis (3,12) left parenthesis 3 comma 12 right parenthesis (3,14) left parenthesis 3 comma 14 right parenthesis (3,7)
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Which of the following ordered pairs is part of the solution set for the equation y=2x+5 ? (1 point) Responses (1,7) left parenthesis 1 comma 7 right parenthesis (1,2) left parenthesis 1 comma 2 right parenthesis (7,1) left parenthesis 7 comma 1 right parenthesis (3,−1)
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Which of the following ordered pairs is part of the solution set for the equation y=5x^2−2 ? (1 point) Responses (1,5) left parenthesis 1 comma 5 right parenthesis (−1,3) left parenthesis negative 1 comma 3 right parenthesis (−1,43) left parenthesis negative 1 comma 43 right parenthesis (−1,5)
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To determine which of the ordered pairs is a solution to the equation \(3x - 8 = -4y\), we'll substitute the \(x\) and \(y\) values from each ordered pair into the equation and check if the equation holds true.
1. For the pair \((0, -2)\):
\[
3(0) - 8 = -4(-2) \implies -8 = 8 \quad \text{(False)}
\]
2. For the pair \((-1, 1)\):
\[
3(-1) - 8 = -4(1) \implies -3 - 8 = -4 \implies -11 = -4 \quad \text{(False)}
\]
3. For the pair \((1, 1)\):
\[
3(1) - 8 = -4(1) \implies 3 - 8 = -4 \implies -5 = -4 \quad \text{(False)}
\]
4. For the pair \((0, 2)\):
\[
3(0) - 8 = -4(2) \implies -8 = -8 \quad \text{(True)}
\]
The only ordered pair that is a solution to the equation \(3x - 8 = -4y\) is \((0, 2)\).
1. For the pair \((0, -2)\):
\[
3(0) - 8 = -4(-2) \implies -8 = 8 \quad \text{(False)}
\]
2. For the pair \((-1, 1)\):
\[
3(-1) - 8 = -4(1) \implies -3 - 8 = -4 \implies -11 = -4 \quad \text{(False)}
\]
3. For the pair \((1, 1)\):
\[
3(1) - 8 = -4(1) \implies 3 - 8 = -4 \implies -5 = -4 \quad \text{(False)}
\]
4. For the pair \((0, 2)\):
\[
3(0) - 8 = -4(2) \implies -8 = -8 \quad \text{(True)}
\]
The only ordered pair that is a solution to the equation \(3x - 8 = -4y\) is \((0, 2)\).
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GPT-4o mini
To determine which of the ordered pairs is a solution to the equation \(1.5x - 2y = 8\), we will substitute the \(x\) and \(y\) values from each ordered pair into the equation and check if the equation holds true.
1. For the pair \((4, -7)\) (Mary):
\[
1.5(4) - 2(-7) = 8 \\
6 + 14 = 8 \\
20 \neq 8 \quad \text{(False)}
\]
2. For the pair \((-4, -7)\) (Sam):
\[
1.5(-4) - 2(-7) = 8 \\
-6 + 14 = 8 \\
8 = 8 \quad \text{(True)}
\]
3. For the pair \((4, 7)\) (Fiona):
\[
1.5(4) - 2(7) = 8 \\
6 - 14 = 8 \\
-8 \neq 8 \quad \text{(False)}
\]
4. For the pair \((-4, 7)\) (Peter):
\[
1.5(-4) - 2(7) = 8 \\
-6 - 14 = 8 \\
-20 \neq 8 \quad \text{(False)}
\]
The only ordered pair that is a solution to the equation \(1.5x - 2y = 8\) is \((-4, -7)\) as suggested by Sam.
1. For the pair \((4, -7)\) (Mary):
\[
1.5(4) - 2(-7) = 8 \\
6 + 14 = 8 \\
20 \neq 8 \quad \text{(False)}
\]
2. For the pair \((-4, -7)\) (Sam):
\[
1.5(-4) - 2(-7) = 8 \\
-6 + 14 = 8 \\
8 = 8 \quad \text{(True)}
\]
3. For the pair \((4, 7)\) (Fiona):
\[
1.5(4) - 2(7) = 8 \\
6 - 14 = 8 \\
-8 \neq 8 \quad \text{(False)}
\]
4. For the pair \((-4, 7)\) (Peter):
\[
1.5(-4) - 2(7) = 8 \\
-6 - 14 = 8 \\
-20 \neq 8 \quad \text{(False)}
\]
The only ordered pair that is a solution to the equation \(1.5x - 2y = 8\) is \((-4, -7)\) as suggested by Sam.
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GPT-4o mini
To determine which of the ordered pairs is part of the solution set for the equation \(y = 4x + 2\), we need to substitute \(x\) from each pair into the equation and see if the resulting \(y\) matches the \(y\) value in the pair.
1. For the pair \((3, 45)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(Not a solution; } y = 45\text{)}
\]
2. For the pair \((3, 12)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(Not a solution; } y = 12\text{)}
\]
3. For the pair \((3, 14)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(This is a solution; } y = 14\text{)}
\]
4. For the pair \((3, 7)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(Not a solution; } y = 7\text{)}
\]
Thus, the ordered pair that is part of the solution set for the equation \(y = 4x + 2\) is \((3, 14)\).
1. For the pair \((3, 45)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(Not a solution; } y = 45\text{)}
\]
2. For the pair \((3, 12)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(Not a solution; } y = 12\text{)}
\]
3. For the pair \((3, 14)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(This is a solution; } y = 14\text{)}
\]
4. For the pair \((3, 7)\):
\[
y = 4(3) + 2 = 12 + 2 = 14 \quad \text{(Not a solution; } y = 7\text{)}
\]
Thus, the ordered pair that is part of the solution set for the equation \(y = 4x + 2\) is \((3, 14)\).
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GPT-4o mini
To determine which of the ordered pairs is part of the solution set for the equation \(y = 2x + 5\), we will substitute the \(x\) value from each pair into the equation and check if the resulting \(y\) matches the \(y\) value in the pair.
1. For the pair \((1, 7)\):
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(This is a solution; } y = 7\text{)}
\]
2. For the pair \((1, 2)\):
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(Not a solution; } y = 2\text{)}
\]
3. For the pair \((7, 1)\):
\[
y = 2(7) + 5 = 14 + 5 = 19 \quad \text{(Not a solution; } y = 1\text{)}
\]
4. For the pair \((3, -1)\):
\[
y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(Not a solution; } y = -1\text{)}
\]
The only ordered pair that is part of the solution set for the equation \(y = 2x + 5\) is \((1, 7)\).
1. For the pair \((1, 7)\):
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(This is a solution; } y = 7\text{)}
\]
2. For the pair \((1, 2)\):
\[
y = 2(1) + 5 = 2 + 5 = 7 \quad \text{(Not a solution; } y = 2\text{)}
\]
3. For the pair \((7, 1)\):
\[
y = 2(7) + 5 = 14 + 5 = 19 \quad \text{(Not a solution; } y = 1\text{)}
\]
4. For the pair \((3, -1)\):
\[
y = 2(3) + 5 = 6 + 5 = 11 \quad \text{(Not a solution; } y = -1\text{)}
\]
The only ordered pair that is part of the solution set for the equation \(y = 2x + 5\) is \((1, 7)\).
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GPT-4o mini
To determine which of the ordered pairs is part of the solution set for the equation \(y = 5x^2 - 2\), we will substitute the \(x\) value from each pair into the equation and check if the resulting \(y\) matches the \(y\) value in the pair.
1. For the pair \((1, 5)\):
\[
y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(Not a solution; } y = 5\text{)}
\]
2. For the pair \((-1, 3)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(This is a solution; } y = 3\text{)}
\]
3. For the pair \((-1, 43)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(Not a solution; } y = 43\text{)}
\]
4. For the pair \((-1, 5)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(Not a solution; } y = 5\text{)}
\]
The only ordered pair that is part of the solution set for the equation \(y = 5x^2 - 2\) is \((-1, 3)\).
1. For the pair \((1, 5)\):
\[
y = 5(1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(Not a solution; } y = 5\text{)}
\]
2. For the pair \((-1, 3)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(This is a solution; } y = 3\text{)}
\]
3. For the pair \((-1, 43)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(Not a solution; } y = 43\text{)}
\]
4. For the pair \((-1, 5)\):
\[
y = 5(-1)^2 - 2 = 5(1) - 2 = 5 - 2 = 3 \quad \text{(Not a solution; } y = 5\text{)}
\]
The only ordered pair that is part of the solution set for the equation \(y = 5x^2 - 2\) is \((-1, 3)\).