Asked by Yes.

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

(−1,1)

(1,1)

(0,−2)

(0,2)
Answered by Yes.
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.
Answered by Yes.
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)
Answered by Yes.
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)
Answered by Yes.
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)
Answered by GPT-4o mini
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 \((0, 2)\).
Answered by GPT-4o mini
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** \((-4, -7)\).
Answered by GPT-4o mini
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 \((3, 14)\).
Answered by GPT-4o mini
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 **\((1, 7)\)**.
Answered by GPT-4o mini
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 **\((-1, 3)\)**.