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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

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

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

(0,−2)

9 answers

To determine which of the given ordered pairs \((x, y)\) satisfies the equation \(3x - 8 = -4y\), we can substitute each pair into the equation and check if both sides are equal.

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

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

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

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

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

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.
Peter believes left parenthesis negative 4 comma 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.

Mary believes (4,−7) is a solution.

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

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

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

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

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

The correct solution to the equation \(1.5x - 2y = 8\) is Sam's belief \((-4, -7)\).

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

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

(3,14)
left parenthesis 3 comma 14 right parenthesis

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

(3,12)

To determine which of the given ordered pairs \((x, y)\) is a solution to the equation \(y = 4x + 2\), we will substitute \(x\) from each pair into the equation and check if the calculated \(y\) matches the \(y\) given in the pair.

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

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

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

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

The correct solution that satisfies the equation \(y = 4x + 2\) is \((3, 14)\).

Use the image to answer the question.

A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. A line passes through the first, second, and third quadrants.

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

(1,2)
left parenthesis 1 comma 2 right parenthesis

(3,−1)

To determine which of the given ordered pairs \((x, y)\) 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 calculate the corresponding \(y\) to see if it matches.

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

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

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

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

The correct solution that satisfies the equation \(y = 2x + 5\) is \((1, 7)\).

Use the image to answer the question.

A graph shows both the x-axis and y-axis, ranging from negative 10 to 10 in increments of 5. An upward parabola passes through all four quadrants.

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

(1 point)
Responses

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

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

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

(1,5)

To determine which of the given ordered pairs \((x, y)\) 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 calculate the corresponding \(y\) to see if it matches.

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

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

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

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

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