https://file.aiquickdraw.com/mathbot/file/172548086245881bee9ed.jpg

The image contains a geometry problem and a system of linear equations problem. I'll break down each part and provide solutions.

### 1. Geometry Problem:
The task is to identify which of the shapes can be classified as a rectangle. A rectangle has four right angles.

The shapes provided are:
- Shape 1: A quadrilateral (non-rectangle)
- Shape 2: A rectangle
- Shape 3: A parallelogram (non-rectangle)
- Shape 4: A rectangle

**Solution**:
- **Shape 2** and **Shape 4** can be classified as rectangles because they have four right angles.

### 2. System of Equations Problem:
The problem asks to solve the following system of equations by substitution or elimination.

\[
\begin{align*}
\text{Equation 1:} & \quad 2x + y = 5 \\
\text{Equation 2:} & \quad -3x + 2y = 4
\end{align*}
\]

#### **Step-by-Step Solution:**

**Step 1: Solve for \( y \) in Equation 1.**

\[
y = 5 - 2x
\]

**Step 2: Substitute \( y = 5 - 2x \) into Equation 2.**

\[
-3x + 2(5 - 2x) = 4
\]

**Step 3: Expand and solve for \( x \).**

\[
-3x + 10 - 4x = 4
\]
\[
-7x + 10 = 4
\]
\[
-7x = 4 - 10
\]
\[
-7x = -6
\]
\[
x = \frac{6}{7}
\]

**Step 4: Substitute \( x = \frac{6}{7} \) back into \( y = 5 - 2x \).**

\[
y = 5 - 2\left(\frac{6}{7}\right)
\]
\[
y = 5 - \frac{12}{7}
\]
\[
y = \frac{35}{7} - \frac{12}{7}
\]
\[
y = \frac{23}{7}
\]

**Solution:**
The solution to the system of equations is:
\[
x = \frac{6}{7}, \quad y = \frac{23}{7}
\]

### Do you have any questions or would you like further details?

Here are some related questions that might help:
1. How can you classify different types of quadrilaterals based on their properties?
2. What other methods can be used to solve a system of equations?
3. How do you verify that a solution to a system of equations is correct?
4. Can the solution to a system of equations be represented graphically? How?
5. What are the implications of having no solution or infinitely many solutions in a system of equations?

**Tip:** When solving systems of equations, always double-check your substitution or elimination steps to avoid simple errors.

Identify which of the shapes can be classified as a rectangle. Also, solve the following system of equations: 2x + y = 5 and -3x + 2y = 4.

Learn how to classify shapes as rectangles based on their properties and solve a system of linear equations using substitution and elimination methods. This problem involves concepts from Geometry and Algebra, suitable for students in Grades 7-9.

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