toko alat tulis pak rudi menjual alat tulis berisi buku,spidol,dan tinta dalam 3 jenis paket.paket A, berisi 3 buku 1 spidol 2 tinta seharga 17.200, paket B: 2 buku 2 spidol 3 tinta seharga 19.700, paket C:1 buku 2 spidol 2 tinta seharga 14.000. harga 1 buku 1 spidol dan 1 tinta adalah

Masalah ini dapat diselesaikan dengan sistem persamaan linear tiga variabel. Mari kita definisikan:

- \( x \) = harga 1 buku
- \( y \) = harga 1 spidol
- \( z \) = harga 1 tinta

Dari informasi paket yang diberikan, kita dapat membuat tiga persamaan:

1. Paket A: 3 buku, 1 spidol, 2 tinta seharga 17.200
   \[
   3x + y + 2z = 17.200
   \]

2. Paket B: 2 buku, 2 spidol, 3 tinta seharga 19.700
   \[
   2x + 2y + 3z = 19.700
   \]

3. Paket C: 1 buku, 2 spidol, 2 tinta seharga 14.000
   \[
   x + 2y + 2z = 14.000
   \]

Sekarang, kita memiliki tiga persamaan linear dengan tiga variabel \(x\), \(y\), dan \(z\). Kita akan menyelesaikan sistem persamaan ini untuk menemukan harga masing-masing buku, spidol, dan tinta.

Mari kita selesaikan sistem ini.It seems the computation took too long. Let me simplify the steps manually.

We will use the substitution or elimination method to solve the system of equations:

1. From the third equation \( x + 2y + 2z = 14,000 \), solve for \( x \):
   \[
   x = 14,000 - 2y - 2z
   \]

2. Substitute this expression for \( x \) in the first and second equations:

   - Substitute in \( 3x + y + 2z = 17,200 \):
     \[
     3(14,000 - 2y - 2z) + y + 2z = 17,200
     \]
     Simplify:
     \[
     42,000 - 6y - 6z + y + 2z = 17,200
     \]
     \[
     42,000 - 5y - 4z = 17,200
     \]
     \[
     5y + 4z = 24,800 \quad \text{(Equation 4)}
     \]

   - Substitute in \( 2x + 2y + 3z = 19,700 \):
     \[
     2(14,000 - 2y - 2z) + 2y + 3z = 19,700
     \]
     Simplify:
     \[
     28,000 - 4y - 4z + 2y + 3z = 19,700
     \]
     \[
     28,000 - 2y - z = 19,700
     \]
     \[
     2y + z = 8,300 \quad \text{(Equation 5)}
     \]

Now we have two simpler equations:

1. \( 5y + 4z = 24,800 \)
2. \( 2y + z = 8,300 \)

Let's solve these two equations to find the values of \( y \) and \( z \).It seems the environment has been reset, and the previous code context was lost. Let me quickly rework the final step manually.

We have the two equations:
1. \( 5y + 4z = 24,800 \)
2. \( 2y + z = 8,300 \)

To solve:

1. Multiply the second equation by 4 to eliminate \( z \):
   \[
   8y + 4z = 33,200
   \]

2. Subtract the first equation from the modified second equation:
   \[
   (8y + 4z) - (5y + 4z) = 33,200 - 24,800
   \]
   \[
   3y = 8,400
   \]
   \[
   y = 2,800
   \]

3. Substitute \( y = 2,800 \) into the second equation \( 2y + z = 8,300 \):
   \[
   2(2,800) + z = 8,300
   \]
   \[
   5,600 + z = 8,300
   \]
   \[
   z = 2,700
   \]

4. Finally, substitute \( y = 2,800 \) and \( z = 2,700 \) into the expression for \( x \) from the third equation:
   \[
   x + 2(2,800) + 2(2,700) = 14,000
   \]
   \[
   x + 5,600 + 5,400 = 14,000
   \]
   \[
   x = 3,000
   \]

Thus, the prices are:
- \( x = 3,000 \) (harga 1 buku)
- \( y = 2,800 \) (harga 1 spidol)
- \( z = 2,700 \) (harga 1 tinta)

Do you need further details or have any questions?

Here are five related questions:
1. How do you solve systems of equations using substitution?
2. Can this problem be solved using matrix methods like Gaussian elimination?
3. How can you verify the solution by substitution into the original equations?
4. How does the method of elimination differ from substitution in solving linear systems?
5. What are some real-world applications of solving systems of equations?

**Tip:** Solving systems of equations by substitution is helpful when one variable is easy to isolate.

toko alat tulis pak rudi menjual alat tulis berisi buku, spidol, dan tinta dalam 3 jenis paket. Paket A, berisi 3 buku 1 spidol 2 tinta seharga 17.200, paket B: 2 buku 2 spidol 3 tinta seharga 19.700, paket C: 1 buku 2 spidol 2 tinta seharga 14.000. Harga 1 buku 1 spidol dan 1 tinta adalah

Solve a system of linear equations to determine the price of a book, a marker, and ink. Using algebraic methods such as substitution and elimination, this problem helps to find the prices from three package deals offered at a stationery store. Suitable for Grades 10-12.

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