The price of 17 pens and 9 pencil is 215 rupees and the price of 9 pens

It looks like the information is still incomplete. To solve the system of equations, we need the complete statement for the second equation. A typical form might be something like "the price of 9 pens and some number of pencils is some number of rupees."

Let's assume a potential second part for demonstration purposes. If the second part of your question states, "the price of 9 pens and 5 pencils is 125 rupees," we can proceed as follows:

Let:
- \( P \) be the price of one pen.
- \( Q \) be the price of one pencil.

From the given information, we have:
1. The price of 17 pens and 9 pencils is 215 rupees:
   \[
   17P + 9Q = 215
   \]
2. The price of 9 pens and 5 pencils is 125 rupees:
   \[
   9P + 5Q = 125
   \]

We now have a system of linear equations:

1. \( 17P + 9Q = 215 \)
2. \( 9P + 5Q = 125 \)

Let's solve this system using the method of elimination:

### Step 1: Eliminate \( Q \)

Multiply the second equation by 9:
\[ 81P + 45Q = 1125 \]

Multiply the first equation by 5:
\[ 85P + 45Q = 1075 \]

### Step 2: Subtract the two equations
\[ (81P + 45Q) - (85P + 45Q) = 1125 - 1075 \]
\[ -4P = 50 \]
\[ P = -\frac{50}{-4} \]
\[ P = 12.5 \]

### Step 3: Substitute \( P \) back into one of the original equations to find \( Q \)

Substitute \( P = 12.5 \) into the second equation:
\[ 9(12.5) + 5Q = 125 \]
\[ 112.5 + 5Q = 125 \]
\[ 5Q = 125 - 112.5 \]
\[ 5Q = 12.5 \]
\[ Q = \frac{12.5}{5} \]
\[ Q = 2.5 \]

So, the price of one pen (\( P \)) is 12.5 rupees and the price of one pencil (\( Q \)) is 2.5 rupees.

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**Do you want details or have any questions?**

**Related Questions:**

1. How do we verify the solution to a system of equations?
2. Can the method of substitution be used instead of elimination for solving this system?
3. What are the advantages of using the elimination method over substitution?
4. How can we interpret the solution of this system graphically?
5. What are some other real-life examples of solving systems of linear equations?
6. How do we handle systems of equations with more than two variables?
7. What happens if the system of equations has no solution or infinite solutions?
8. How do we solve systems of equations using matrix operations?

**Tip:** Always double-check your solution by substituting the values back into the original equations to ensure they satisfy both equations.

Learn how to solve a system of linear equations involving the prices of pens and pencils. This problem demonstrates the application of the elimination method to find the prices of individual pens and pencils based on given total costs.

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