Question
Ms. Mac asked her students to determine a solution for 2z5y = 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)
Liam
named a point that is a solution that lies on the graph of the equation.
Marco
named a point that is not a solution and lies above the graph of the equation.
Bella
Thamed a
point that is not a solution and bes below the graph of the equation.
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)
Liam
named a point that is a solution that lies on the graph of the equation.
Marco
named a point that is not a solution and lies above the graph of the equation.
Bella
Thamed a
point that is not a solution and bes below the graph of the equation.
Answers
GPT-4o mini
To determine which of the points proposed by Bella, Marco, and Liam are solutions to the equation \(2z + 5y = 9\), we will plug each point into the equation.
1. **Bella's point: \((-2, 1)\)**
\[
2(-2) + 5(1) = -4 + 5 = 1 \quad (\text{not equal to } 9)
\]
So, \((-2, 1)\) is **not a solution** and lies **below** the graph of the equation.
2. **Marco's point: \((11, 2)\)**
\[
2(11) + 5(2) = 22 + 10 = 32 \quad (\text{not equal to } 9)
\]
So, \((11, 2)\) is **not a solution** and lies **above** the graph of the equation.
3. **Liam's point: \((2, -1)\)**
\[
2(2) + 5(-1) = 4 - 5 = -1 \quad (\text{not equal to } 9)
\]
So, \((2, -1)\) is **not a solution** and lies **below** the graph of the equation.
### Summary:
- Liam: \((2, -1)\) is **not a solution** and lies **below** the graph of the equation.
- Marco: \((11, 2)\) is **not a solution** and lies **above** the graph of the equation.
- Bella: \((-2, 1)\) is **not a solution** and lies **below** the graph of the equation.
Thus, the correct statements would be:
- Liam named a point that is **not a solution** and lies **below** the graph of the equation.
- Marco named a point that is **not a solution** and lies **above** the graph of the equation.
- Bella named a point that is **not a solution** and lies **below** the graph of the equation.
1. **Bella's point: \((-2, 1)\)**
\[
2(-2) + 5(1) = -4 + 5 = 1 \quad (\text{not equal to } 9)
\]
So, \((-2, 1)\) is **not a solution** and lies **below** the graph of the equation.
2. **Marco's point: \((11, 2)\)**
\[
2(11) + 5(2) = 22 + 10 = 32 \quad (\text{not equal to } 9)
\]
So, \((11, 2)\) is **not a solution** and lies **above** the graph of the equation.
3. **Liam's point: \((2, -1)\)**
\[
2(2) + 5(-1) = 4 - 5 = -1 \quad (\text{not equal to } 9)
\]
So, \((2, -1)\) is **not a solution** and lies **below** the graph of the equation.
### Summary:
- Liam: \((2, -1)\) is **not a solution** and lies **below** the graph of the equation.
- Marco: \((11, 2)\) is **not a solution** and lies **above** the graph of the equation.
- Bella: \((-2, 1)\) is **not a solution** and lies **below** the graph of the equation.
Thus, the correct statements would be:
- Liam named a point that is **not a solution** and lies **below** the graph of the equation.
- Marco named a point that is **not a solution** and lies **above** the graph of the equation.
- Bella named a point that is **not a solution** and lies **below** the graph of the equation.