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The problem in the image states:

- Seven cups and eight plates cost ₦1750.
- Eight cups and seven plates cost ₦1700.
- Calculate the cost of a cup and a plate.

Let's define:
- \( x \) as the cost of one cup.
- \( y \) as the cost of one plate.

From the given information, we can form the following system of equations:

\[
7x + 8y = 1750
\]
\[
8x + 7y = 1700
\]

We can now solve this system of linear equations to find the values of \( x \) (the cost of a cup) and \( y \) (the cost of a plate). I'll solve it now.The solution to the system of equations is:

- The cost of one cup is ₦90.
- The cost of one plate is ₦140.

Would you like a more detailed explanation or have any questions?

Here are five related questions to expand on this:

1. How can you check the solution for the cost of the cup and plate using substitution?
2. What would be the total cost of 10 cups and 5 plates?
3. How do you solve a system of equations using substitution or elimination methods?
4. Can you calculate the percentage increase if the cost of a cup increases to ₦100?
5. How does the cost of cups and plates change if the prices of both are increased by 10%?

**Tip:** When solving a system of linear equations, the elimination method can often simplify the process if substitution seems complex.

Seven cups and eight plates cost ₦1750. Eight cups and seven plates cost ₦1700. Calculate the cost of a cup and a plate.

Learn how to solve a system of linear equations to find the cost of a cup and a plate. This problem involves solving two equations with two variables using the elimination method. Suitable for students in Grades 9-10.

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