Determine which of the following ordered pairs is a solution to the equation 8−2y=4x2

Question

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Option #1: (0,8)


Option #2: (−1,2)


Option #3: (4,0)


(1 point)
Option #
is a solution to the equation.

Answer 1

To determine which ordered pair is a solution to the equation \( 8 - 2y = 4x^2 \), we need to substitute the values of \( x \) and \( y \) in each option into the equation and see if it holds true.

Option #1: (0, 8)

• Substitute \( x = 0 \) and \( y = 8 \): \[ 8 - 2(8) = 4(0)^2 \ 8 - 16 = 0 \ -8 \neq 0 \quad (\text{not a solution}) \]

Option #2: (-1, 2)

• Substitute \( x = -1 \) and \( y = 2 \): \[ 8 - 2(2) = 4(-1)^2 \ 8 - 4 = 4(1) \ 4 = 4 \quad (\text{is a solution}) \]

Option #3: (4, 0)

• Substitute \( x = 4 \) and \( y = 0 \): \[ 8 - 2(0) = 4(4)^2 \ 8 - 0 = 4(16) \ 8 = 64 \quad (\text{not a solution}) \]

After checking all the options, we find that:

Option #2: (-1, 2) is a solution to the equation \( 8 - 2y = 4x^2 \).

Answer 2

Ms. Smith asked her students to determine a solution for 3x−4y=8
. Which of the following students found the correct solution???

Student #1: Linda believes (1,−4)
is a solution to the equation.

Student #2: Nathan believes (5,3)
is a solution to the equation.

Student #3: Gary believes (4,1)
is a solution to the equation.

(1 point)
Student #
is correct.

Answer 3

To determine which student found the correct solution for the equation \( 3x - 4y = 8 \), we will substitute the values of \( x \) and \( y \) from each student's proposed solution into the equation and check if it holds true.

Student #1: Linda (1, -4)

• Substitute \( x = 1 \) and \( y = -4 \): \[ 3(1) - 4(-4) = 8 \ 3 + 16 = 8 \ 19 \neq 8 \quad (\text{not a solution}) \]

Student #2: Nathan (5, 3)

• Substitute \( x = 5 \) and \( y = 3 \): \[ 3(5) - 4(3) = 8 \ 15 - 12 = 8 \ 3 \neq 8 \quad (\text{not a solution}) \]

Student #3: Gary (4, 1)

• Substitute \( x = 4 \) and \( y = 1 \): \[ 3(4) - 4(1) = 8 \ 12 - 4 = 8 \ 8 = 8 \quad (\text{is a solution}) \]

Based on our checks:

Student #3 (Gary) is correct.

Answer 4

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, third, and fourth quadrants.

Which of the following ordered pairs is part of the solution set for the equation y=3x−4
?

Option #1: (−1,0)


Option #2: (0,−4)


Option #3: (3,4)


(1 point)
Option #
is part of the solution set for the equation.

Answer 5

To determine which of the ordered pairs is part of the solution set for the equation \( y = 3x - 4 \), we will substitute the values of \( x \) and \( y \) from each option into the equation and see if the equation holds true.

Option #1: \( (-1, 0) \)

• Substitute \( x = -1 \): \[ y = 3(-1) - 4 \ y = -3 - 4 \ y = -7 \quad \text{(not } (−1, 0) \text{)} \]

Option #2: \( (0, -4) \)

• Substitute \( x = 0 \): \[ y = 3(0) - 4 \ y = 0 - 4 \ y = -4 \quad \text{(is } (0, -4) \text{)} \]

Option #3: \( (3, 4) \)

• Substitute \( x = 3 \): \[ y = 3(3) - 4 \ y = 9 - 4 \ y = 5 \quad \text{(not } (3, 4) \text{)} \]

After evaluating all options, we find that:

Option #2: \( (0, -4) \) is part of the solution set for the equation \( y = 3x - 4 \).

Answer 6

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 that passes through all four quadrants is depicted.

Which of the following ordered pairs is part of the solution set for the equation y=3x2−4
?

Option #1: (−2,−8)


Option #2: (2,8)


Option #3: (−4,0)


(1 point)
Option #
is part of the solution set for the equation.

Answer 7

To determine which ordered pair is part of the solution set for the equation \( y = 3x^2 - 4 \), we will substitute the values of \( x \) into the equation and compare the resulting \( y \) value with the given \( y \) in each option.

Option #1: \( (-2, -8) \)

• Substitute \( x = -2 \): \[ y = 3(-2)^2 - 4 \ y = 3(4) - 4 \ y = 12 - 4 \ y = 8 \quad \text{(the ordered pair is } (-2, 8) \text{, not } (-2, -8)\text{)} \]

Option #2: \( (2, 8) \)

• Substitute \( x = 2 \): \[ y = 3(2)^2 - 4 \ y = 3(4) - 4 \ y = 12 - 4 \ y = 8 \quad \text{(the ordered pair is } (2, 8) \text{, which matches.)} \]

Option #3: \( (-4, 0) \)

• Substitute \( x = -4 \): \[ y = 3(-4)^2 - 4 \ y = 3(16) - 4 \ y = 48 - 4 \ y = 44 \quad \text{(the ordered pair is } (-4, 44) \text{, not } (-4, 0)\text{)} \]

After evaluating all the options, we find that:

Option #2: \( (2, 8) \) is part of the solution set for the equation \( y = 3x^2 - 4 \).

Answer 8

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=3x2−4
?

Option #1: (−1,1)

Option #2: (0,3)

Option #3: (3,1)

(1 point)
Option #
is part of the solution set for the equation.

Answer 9

To determine which ordered pair is part of the solution set for the equation \( y = 3x^2 - 4 \), we will substitute the values of \( x \) from each option into the equation and see if the resulting value of \( y \) matches the \( y \) value given in the ordered pair.

Option #1: \( (-1, 1) \)

• Substitute \( x = -1 \): \[ y = 3(-1)^2 - 4 \ y = 3(1) - 4 \ y = 3 - 4 \ y = -1 \quad \text{(not } (−1, 1) \text{)} \]

Option #2: \( (0, 3) \)

• Substitute \( x = 0 \): \[ y = 3(0)^2 - 4 \ y = 3(0) - 4 \ y = 0 - 4 \ y = -4 \quad \text{(not } (0, 3) \text{)} \]

Option #3: \( (3, 1) \)

• Substitute \( x = 3 \): \[ y = 3(3)^2 - 4 \ y = 3(9) - 4 \ y = 27 - 4 \ y = 23 \quad \text{(not } (3, 1) \text{)} \]

After checking all the options:

• Option #1: \( (-1, 1) \) results in \( -1 \).
• Option #2: \( (0, 3) \) results in \( -4 \).
• Option #3: \( (3, 1) \) results in \( 23 \).

None of the given options are solutions to the equation \( y = 3x^2 - 4 \).

If you're looking for an ordered pair that is indeed a solution to the equation, you may consider the following process:

1. Substitute \( x \) values into the equation and solve for \( y \).
2. Check if the resulting \( y \) values match with options provided.

If you need any additional help or clarification, feel free to ask!