Determine which of the following ordered pairs is a solution to the equation 3x−8=−4y .

Question

Responses:

(−1,1)

(1,1)

(0,−2)

(0,2)

Answer 1

To determine which ordered pair is a solution to the equation \( 3x - 8 = -4y \), we can substitute each pair into the equation and see if it holds true.

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

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

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

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

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?
Responses:

Sam believes (−4,−7) is a solution.

Peter believes (−4,7) is a solution.

Fiona believes (4,7) is a solution.

Mary believes (4,−7) is a solution.

Answer 3

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

1. For Sam's pair \((-4, -7)\): \[ x = -4, \quad y = -7 \] Substituting into the equation: \[ 1.5(-4) - 2(-7) = 8 \] \[ -6 + 14 = 8 \] \[ 8 = 8 \quad \text{(is a solution)} \]

2. For Peter's pair \((-4, 7)\): \[ x = -4, \quad y = 7 \] Substituting into the equation: \[ 1.5(-4) - 2(7) = 8 \] \[ -6 - 14 = 8 \] \[ -20 \neq 8 \quad \text{(not a solution)} \]

3. For Fiona's pair \((4, 7)\): \[ x = 4, \quad y = 7 \] Substituting into the equation: \[ 1.5(4) - 2(7) = 8 \] \[ 6 - 14 = 8 \] \[ -8 \neq 8 \quad \text{(not a solution)} \]

4. For Mary's pair \((4, -7)\): \[ x = 4, \quad y = -7 \] Substituting into the equation: \[ 1.5(4) - 2(-7) = 8 \] \[ 6 + 14 = 8 \] \[ 20 \neq 8 \quad \text{(not a solution)} \]

After checking all pairs, the only correct solution is Sam's pair \((-4, -7)\).

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.
Responses:

(3,12)

(3,45)

(3,7)

(3,14)

Answer 5

To determine which ordered pair is part of the solution set for the equation \( y = 4x + 2 \), we need to substitute \( x \) from each pair into the equation and check if the corresponding \( y \) is equal to \( 4x + 2 \).

1. For the pair \((3, 12)\): \[ x = 3 \] Substituting into the equation: \[ y = 4(3) + 2 = 12 + 2 = 14 \] \[ 12 \neq 14 \quad \text{(not a solution)} \]

2. For the pair \((3, 45)\): \[ x = 3 \] Substituting into the equation: \[ y = 4(3) + 2 = 12 + 2 = 14 \] \[ 45 \neq 14 \quad \text{(not a solution)} \]

3. For the pair \((3, 7)\): \[ x = 3 \] Substituting into the equation: \[ y = 4(3) + 2 = 12 + 2 = 14 \] \[ 7 \neq 14 \quad \text{(not a solution)} \]

4. For the pair \((3, 14)\): \[ x = 3 \] Substituting into the equation: \[ y = 4(3) + 2 = 12 + 2 = 14 \] \[ 14 = 14 \quad \text{(is a solution)} \]

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

Answer 6

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

Responses:

(1,7)

(3,−1)

(7,1)

(1,2)

Answer 7

To determine which ordered pair 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 given \( y \).

1. For the pair \((1, 7)\): \[ x = 1 \] Substituting into the equation: \[ y = 2(1) + 5 = 2 + 5 = 7 \] \[ 7 = 7 \quad \text{(is a solution)} \]

2. For the pair \((3, -1)\): \[ x = 3 \] Substituting into the equation: \[ y = 2(3) + 5 = 6 + 5 = 11 \] \[ -1 \neq 11 \quad \text{(not a solution)} \]

3. For the pair \((7, 1)\): \[ x = 7 \] Substituting into the equation: \[ y = 2(7) + 5 = 14 + 5 = 19 \] \[ 1 \neq 19 \quad \text{(not a solution)} \]

4. For the pair \((1, 2)\): \[ x = 1 \] Substituting into the equation: \[ y = 2(1) + 5 = 2 + 5 = 7 \] \[ 2 \neq 7 \quad \text{(not a solution)} \]

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

Answer 8

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

Responses:

(1,5)

(−1,3)

(−1,5)

(−1,43)

Answer 9

To determine which ordered pair 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 given \( y \).

1. For the pair \((1, 5)\): \[ x = 1 \] Substituting into the equation: \[ y = 5(1^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \] \[ 5 \neq 3 \quad \text{(not a solution)} \]

2. For the pair \((-1, 3)\): \[ x = -1 \] Substituting into the equation: \[ y = 5(-1^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \] \[ 3 = 3 \quad \text{(is a solution)} \]

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

4. For the pair \((-1, 43)\): \[ x = -1 \] Using the same \( x \): \[ y = 5(-1^2) - 2 = 5(1) - 2 = 5 - 2 = 3 \] \[ 43 \neq 3 \quad \text{(not a solution)} \]

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