Question

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

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

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

(0,−2)

Answer 1

To determine which ordered pair \((x, y)\) 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 see if it holds true.

1. For the pair \((-1, 1)\): \[ 3(-1) - 8 = -4(1) \ -3 - 8 = -4 \ -11 \neq -4 \quad (\text{not a solution}) \]

2. For the pair \((1, 1)\): \[ 3(1) - 8 = -4(1) \ 3 - 8 = -4 \ -5 \neq -4 \quad (\text{not a solution}) \]

3. For the pair \((0, 2)\): \[ 3(0) - 8 = -4(2) \ 0 - 8 = -8 \ -8 = -8 \quad (\text{is a solution}) \]

4. For the pair \((0, -2)\): \[ 3(0) - 8 = -4(-2) \ 0 - 8 = 8 \ -8 \neq 8 \quad (\text{not a solution}) \]

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

Answer 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.

Sam believes (−4,−7) is a solution.
Sam believes left parenthesis negative 4 comma negative 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.

Mary believes (4,−7) is a solution.

Answer 3

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

1. For Fiona’s pair \((4, 7)\): \[ 1.5(4) - 2(7) = 8 \ 6 - 14 = 8 \ -8 \neq 8 \quad (\text{not a solution}) \]

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

3. For Peter’s pair \((-4, 7)\): \[ 1.5(-4) - 2(7) = 8 \ -6 - 14 = 8 \ -20 \neq 8 \quad (\text{not a solution}) \]

4. For Mary’s pair \((4, -7)\): \[ 1.5(4) - 2(-7) = 8 \ 6 + 14 = 8 \ 20 \neq 8 \quad (\text{not a solution}) \]

The only ordered pair that is a solution to the equation \(1.5x - 2y = 8\) is \((-4, -7)\) as proposed by Sam.

Answer 4

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)

Answer 5

To determine which of the ordered pairs \((x, y)\) is part of the solution set for the equation \(y = 4x + 2\), we can substitute \(x = 3\) into the equation and calculate the corresponding \(y\) value. Then we'll compare that value to the \(y\) values in the ordered pairs provided.

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

Now we can compare this result with the \(y\) values in the options:

1. For \((3, 7)\): \(y = 7 \quad (\text{not a solution})\)
2. For \((3, 14)\): \(y = 14 \quad (\text{is a solution})\)
3. For \((3, 45)\): \(y = 45 \quad (\text{not a solution})\)
4. For \((3, 12)\): \(y = 12 \quad (\text{not a solution})\)

The ordered pair that is part of the solution set for the equation \(y = 4x + 2\) is \((3, 14)\).