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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 parenthesis 0 comma 2 right parenthesis

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

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

(1,1)

9 answers

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

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

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

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

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

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

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.

To determine which of the given ordered pairs is a solution to the equation \(1.5x - 2y = 8\), we will substitute the values of \(x\) and \(y\) from each ordered pair into the equation and check if the equation holds true.

  1. For \((4, -7)\): \[ 1.5(4) - 2(-7) = 8 \ 6 + 14 = 8 \ 20 \neq 8 \quad \text{(False)} \]

  2. For \((-4, -7)\): \[ 1.5(-4) - 2(-7) = 8 \ -6 + 14 = 8 \ 8 = 8 \quad \text{(True)} \]

  3. For \((4, 7)\): \[ 1.5(4) - 2(7) = 8 \ 6 - 14 = 8 \ -8 \neq 8 \quad \text{(False)} \]

  4. For \((-4, 7)\): \[ 1.5(-4) - 2(7) = 8 \ -6 - 14 = 8 \ -20 \neq 8 \quad \text{(False)} \]

The only ordered pair that satisfies the equation \(1.5x - 2y = 8\) is \((-4, -7)\). Therefore, Sam is correct in believing that \((-4, -7)\) is a solution.

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

(3,12)
left parenthesis 3 comma 12 right parenthesis

(3,7)
left parenthesis 3 comma 7 right parenthesis

(3,45)
left parenthesis 3 comma 45 right parenthesis

(3,14)

To determine which of the given ordered pairs is a part of the solution set for the equation \(y = 4x + 2\), we will plug in the \(x\) values from each ordered pair into the equation and check if the resulting \(y\) value matches.

  1. For \((3, 12)\): \[ y = 4(3) + 2 \ y = 12 + 2 \ y = 14 \quad \text{(Does not match; 12 ≠ 14)} \]

  2. For \((3, 7)\): \[ y = 4(3) + 2 \ y = 12 + 2 \ y = 14 \quad \text{(Does not match; 7 ≠ 14)} \]

  3. For \((3, 45)\): \[ y = 4(3) + 2 \ y = 12 + 2 \ y = 14 \quad \text{(Does not match; 45 ≠ 14)} \]

  4. For \((3, 14)\): \[ y = 4(3) + 2 \ y = 12 + 2 \ y = 14 \quad \text{(Matches; 14 = 14)} \]

The only ordered pair that satisfies the equation \(y = 4x + 2\) is \((3, 14)\).

Which of the following ordered pairs is part of the solution set for the equation y=2x+5 ?

(1 point)
Responses

(7,1)
left parenthesis 7 comma 1 right parenthesis

(1,7)
left parenthesis 1 comma 7 right parenthesis

(3,−1)
left parenthesis 3 comma negative 1 right parenthesis

(1,2)

To determine which of the given ordered pairs is part of the solution set for the equation \(y = 2x + 5\), we will substitute the values of \(x\) and \(y\) from each ordered pair into the equation and check if the equation holds true.

  1. For \((7, 1)\): \[ y = 2(7) + 5 \ y = 14 + 5 \ y = 19 \quad \text{(Does not match; 1 ≠ 19)} \]

  2. For \((1, 7)\): \[ y = 2(1) + 5 \ y = 2 + 5 \ y = 7 \quad \text{(Matches; 7 = 7)} \]

  3. For \((3, -1)\): \[ y = 2(3) + 5 \ y = 6 + 5 \ y = 11 \quad \text{(Does not match; -1 ≠ 11)} \]

  4. For \((1, 2)\): \[ y = 2(1) + 5 \ y = 2 + 5 \ y = 7 \quad \text{(Does not match; 2 ≠ 7)} \]

The only ordered pair that satisfies the equation \(y = 2x + 5\) is \((1, 7)\).

Which of the following ordered pairs is part of the solution set for the equation y=5x2−2 ?

(1 point)
Responses

(−1,3)
left parenthesis negative 1 comma 3 right parenthesis

(1,5)
left parenthesis 1 comma 5 right parenthesis

(−1,43)
left parenthesis negative 1 comma 43 right parenthesis

(−1,5)

To determine which of the given ordered pairs is part of the solution set for the equation \(y = 5x^2 - 2\), we will substitute the \(x\) values from each ordered pair into the equation and check if the calculated \(y\) value matches the \(y\) value in the ordered pair.

  1. For \((-1, 3)\): \[ y = 5(-1)^2 - 2 \ y = 5(1) - 2 \ y = 5 - 2 = 3 \quad \text{(Matches; 3 = 3)} \]

  2. For \((1, 5)\): \[ y = 5(1)^2 - 2 \ y = 5(1) - 2 \ y = 5 - 2 = 3 \quad \text{(Does not match; 5 ≠ 3)} \]

  3. For \((-1, 43)\): \[ y = 5(-1)^2 - 2 \ y = 5(1) - 2 \ y = 5 - 2 = 3 \quad \text{(Does not match; 43 ≠ 3)} \]

  4. For \((-1, 5)\): \[ y = 5(-1)^2 - 2 \ y = 5(1) - 2 \ y = 5 - 2 = 3 \quad \text{(Does not match; 5 ≠ 3)} \]

The only ordered pair that satisfies the equation \(y = 5x^2 - 2\) is \((-1, 3)\).