Question

Ms.Mac asked her students to determine a solution for 2x -5 =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
Blank named a point That
Is a solution that lies on the graph of the equation. Blank named a point that is not a solution and lives above the graft of the equation. The point name a point that is not a solution and lasts below the graph of the equation.
Liam Marco. Bella

Answer 1

Let's start by solving the equation \(2x - 5 = 9\) for \(x\):

1. Add 5 to both sides:
\[
2x - 5 + 5 = 9 + 5
\]
\[
2x = 14
\]

2. Divide both sides by 2:
\[
x = 7
\]

The solution to the equation is \(x = 7\). Now we will check each of the points provided to see if they are solutions.

1. **Bella believes (-2, 1) is a solution:**
- Substitute \(x = -2\) into the equation \(y = 2x - 5\):
\[
y = 2(-2) - 5 = -4 - 5 = -9
\]
- Since \(y\) does not equal 1, this point is **not a solution**.

2. **Marco believes (11, 2) is a solution:**
- Substitute \(x = 11\):
\[
y = 2(11) - 5 = 22 - 5 = 17
\]
- Since \(y\) does not equal 2, this point is **not a solution**.

3. **Liam believes (2, -1) is a solution:**
- Substitute \(x = 2\):
\[
y = 2(2) - 5 = 4 - 5 = -1
\]
- Since \(y\) equals -1, this point **is a solution**.

### Summary of findings:

- **Liam's point (2, -1)** is a solution to the equation.
- **Bella's point (-2, 1)** is not a solution and is **below** the graph of the equation since \(y = -9 < 1\).
- **Marco's point (11, 2)** is also not a solution and is **above** the graph of the equation since \(y = 17 > 2\).

### Answering the blanks:
- A point that is a solution: **(2, -1)** (from Liam)
- A point that is not a solution and lies above the graph: **(11, 2)** (from Marco)
- A point that is not a solution and lies below the graph: **(-2, 1)** (from Bella)