Question
Ms. Mac asked her students to determine a solution for 2z-5y = 9
Bella believes (-2, 1) is a solution to the equation.
Marco believes (11, 2) is a solution to the equation.
Liam believes (2,-1)is a solution to the equation.
(1 point)
named a point that is a solution that lies on the graph of the equation
named a point that is not a solution and lies above the graph of the equation.
inamed a
point that is not a solution and lies below the graph of the equation.
#Marco
Liam
#Bella
Bella believes (-2, 1) is a solution to the equation.
Marco believes (11, 2) is a solution to the equation.
Liam believes (2,-1)is a solution to the equation.
(1 point)
named a point that is a solution that lies on the graph of the equation
named a point that is not a solution and lies above the graph of the equation.
inamed a
point that is not a solution and lies below the graph of the equation.
#Marco
Liam
#Bella
Answers
GPT-4o mini
To determine which of the suggested points are solutions to the equation \(2z - 5y = 9\), we will substitute each point into the equation.
1. **Bella's point: (-2, 1)**
Substitute \(z = -2\) and \(y = 1\):
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad (\text{not a solution})
\]
2. **Marco's point: (11, 2)**
Substitute \(z = 11\) and \(y = 2\):
\[
2(11) - 5(2) = 22 - 10 = 12 \quad (\text{not a solution})
\]
3. **Liam's point: (2, -1)**
Substitute \(z = 2\) and \(y = -1\):
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad (\text{is a solution})
\]
### Summary:
- **A point that is a solution:** (2, -1) (Liam's point)
- **A point that is not a solution (lies above the graph):** Any point with a higher \(z\) value for a given \(y\). For example, we can use (11, 2) for this purpose, since \(2(11) - 5(2) = 12\) is greater than 9.
- **A point that is not a solution (lies below the graph):** For example, (0, 2) is below the graph because when we substitute \(z = 0\) and \(y = 2\):
\[
2(0) - 5(2) = -10 \quad (\text{not a solution and lies below the graph})
\]
In conclusion:
1. Solution point: (2, -1) [Liam]
2. Not a solution above: (11, 2) [Marco]
3. Not a solution below: (0, 2) [Derived example]
If questions require pointing to specific students:
- Points from the exercise:
- Marco’s point (11, 2)
- Bella's point (-2, 1) can be mentioned for being below the graph.
However, if strictly adhering to the provided students:
- Solution: Liam (2, -1)
- Above: Marco (11, 2)
- Below: Bella (-2, 1)
Please inform if altered values or different cases are needed!
1. **Bella's point: (-2, 1)**
Substitute \(z = -2\) and \(y = 1\):
\[
2(-2) - 5(1) = -4 - 5 = -9 \quad (\text{not a solution})
\]
2. **Marco's point: (11, 2)**
Substitute \(z = 11\) and \(y = 2\):
\[
2(11) - 5(2) = 22 - 10 = 12 \quad (\text{not a solution})
\]
3. **Liam's point: (2, -1)**
Substitute \(z = 2\) and \(y = -1\):
\[
2(2) - 5(-1) = 4 + 5 = 9 \quad (\text{is a solution})
\]
### Summary:
- **A point that is a solution:** (2, -1) (Liam's point)
- **A point that is not a solution (lies above the graph):** Any point with a higher \(z\) value for a given \(y\). For example, we can use (11, 2) for this purpose, since \(2(11) - 5(2) = 12\) is greater than 9.
- **A point that is not a solution (lies below the graph):** For example, (0, 2) is below the graph because when we substitute \(z = 0\) and \(y = 2\):
\[
2(0) - 5(2) = -10 \quad (\text{not a solution and lies below the graph})
\]
In conclusion:
1. Solution point: (2, -1) [Liam]
2. Not a solution above: (11, 2) [Marco]
3. Not a solution below: (0, 2) [Derived example]
If questions require pointing to specific students:
- Points from the exercise:
- Marco’s point (11, 2)
- Bella's point (-2, 1) can be mentioned for being below the graph.
However, if strictly adhering to the provided students:
- Solution: Liam (2, -1)
- Above: Marco (11, 2)
- Below: Bella (-2, 1)
Please inform if altered values or different cases are needed!