https://file.aiquickdraw.com/mathbot/file/1727103740676v8ull3wp.jpg

Let's break down the problem in the image. 

The table provides the following dataLet's break down the problem in the image. 

The table provides the following 

|                    | First delivery | Second delivery |
|--------------------|----------------|-----------------|
| **Number of large boxes** | 5              | 3               |
| **Number of small boxes** | 2              | 8               |
| **Total weight (kg)**     | 102            | 153             |

We are asked to:

### (a) Write a system of equations to find the weight of each type of box:
Let:
- \( x \) be the weight (in kilograms) of each large box.
- \( y \) be the weight (in kilograms) of each small box.

For the first delivery:
\[
5x + 2y = 102
\]
For the second delivery:
\[
3x + 8y = 153
\]

Thus, the system of equations is:
\[
\begin{aligned}
5x + 2y &= 102 \\
3x + 8y &= 153
\end{aligned}
\]

### (b) Solve for \( x \) and \( y \):
We will solve this system of equations using substitution or elimination. Let me calculate that for you.The solution to the system of equations is:

- The weight of each large box (\( x \)) is 15 kilograms.
- The weight of each small box (\( y \)) is \( \frac{27}{2} \) kilograms, or 13.5 kilograms.

Would you like further details or any clarifications?

Here are 5 related questions to deepen your understanding:
1. How can we verify the solution by substituting the values back into the original equations?
2. Can you express the solution graphically by plotting the lines for both equations?
3. How would the system change if the number of large and small boxes in a third delivery were added?
4. What methods besides substitution or elimination could be used to solve the system of equations?
5. How does the concept of systems of linear equations apply to other real-life situations?

**Tip:** Always double-check your solution by substituting the values back into the original equations to verify their accuracy.

Write a system of equations that could be used to find the weight (in kilograms) of each type of box. How much does each type of box weigh (in kilograms)?

Learn how to solve a system of linear equations to determine the weight of large and small boxes using substitution and elimination. The problem involves two deliveries with different numbers of boxes and total weights, perfect for students in Grades 7-10.

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