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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

Fiona believes (4,7) is a solution.
Fiona believes left parenthesis 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.
Mary believes left parenthesis 4 comma negative 7 right parenthesis is a solution.

Peter believes (−4,7) is a solution.

7 answers

To determine which pair is a solution for the equation \(1.5x - 2y = 8\), we can substitute each pair of values into the equation and see if the equation holds true.

  1. Fiona's solution (4, 7): \[ 1.5(4) - 2(7) = 6 - 14 = -8 \quad (\text{Not a solution}) \]

  2. Sam's solution (-4, -7): \[ 1.5(-4) - 2(-7) = -6 + 14 = 8 \quad (\text{This is a solution}) \]

  3. Mary's solution (4, -7): \[ 1.5(4) - 2(-7) = 6 + 14 = 20 \quad (\text{Not a solution}) \]

  4. Peter's solution (-4, 7): \[ 1.5(-4) - 2(7) = -6 - 14 = -20 \quad (\text{Not a solution}) \]

The only solution that satisfies the equation \(1.5x - 2y = 8\) is Sam's belief 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

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

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

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

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

To determine which ordered pair is part of the solution set for the equation \(y = 4x + 2\), we will substitute \(x = 3\) into the equation and find the corresponding value of \(y\).

Substituting \(x = 3\): \[ y = 4(3) + 2 = 12 + 2 = 14 \]

So, when \(x = 3\), \(y = 14\). Therefore, the ordered pair \((3, 14)\) is a solution of the equation.

Now, let’s check each option:

  1. \((3, 45)\): \[ \text{Not a solution, since } y \neq 14. \]

  2. \((3, 12)\): \[ \text{Not a solution, since } y \neq 14. \]

  3. \((3, 7)\): \[ \text{Not a solution, since } y \neq 14. \]

  4. \((3, 14)\): \[ \text{This is a solution, since } y = 14. \]

The correct option is \((3, 14)\).

Use the image to answer the question.

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

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

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

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

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

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

  2. For (3, −1): \[ y = 2(3) + 5 = 6 + 5 = 11 \quad (\text{not a solution}) \]

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

  4. For (1, 7): \[ y = 2(1) + 5 = 2 + 5 = 7 \quad (\text{this is a solution}) \]

The ordered pair that is part of the solution set for the equation \(y = 2x + 5\) is \((1, 7)\).

Use the image to answer the question.

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

(1 point)
Responses

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

(−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

To determine which ordered pair is part of the solution set for the equation \(y = 5x^2 - 2\), we will evaluate each pair by substituting the \(x\) values into the equation and checking if the resulting \(y\) values match.

  1. For (1, 5): \[ y = 5(1^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (\text{not a solution since } y \neq 5) \]

  2. For (−1, 43): \[ y = 5((-1)^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (\text{not a solution since } y \neq 43) \]

  3. For (−1, 5): \[ y = 5((-1)^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (\text{not a solution since } y \neq 5) \]

  4. For (−1, 3): \[ y = 5((-1)^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \quad (\text{this is a solution since } y = 3) \]

The ordered pair that is part of the solution set for the equation \(y = 5x^2 - 2\) is \((-1, 3)\).