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The image you've uploaded contains problems from a chapter titled **"Sistem Persamaan Linear dan Matriks"** (Linear Systems and Matrices). Below is a breakdown of each question from the image:

### Question 6:
- **(a)**: "Tentukan persamaan linear dalam variabel \( x \) dan \( y \) yang memiliki solusi umum \( x = 5 + 2t \), \( y = t \)."  
   *Translation*: Determine the linear equation in variables \( x \) and \( y \) with the general solution \( x = 5 + 2t \), \( y = t \).

- **(b)**: "Tunjukkan bahwa \( x = t \), \( y = \frac{1}{2} t - \frac{5}{2} \) juga merupakan solusi umum untuk persamaan \( (x, y) \)."  
   *Translation*: Show that \( x = t \), \( y = \frac{1}{2} t - \frac{5}{2} \) is also a general solution for the equation in \( (x, y) \).

### Question 7:
- The question describes a quadratic curve \( y = ax^2 + bx + c \) that passes through three points \( (x_1, y_1), (x_2, y_2), (x_3, y_3) \), and asks to show that the coefficients \( a \), \( b \), and \( c \) form the solution of the linear system represented by a 3x3 matrix:
  \[
  \begin{pmatrix}
  x_1^2 & x_1 & 1 \\
  x_2^2 & x_2 & 1 \\
  x_3^2 & x_3 & 1
  \end{pmatrix}
  \begin{pmatrix}
  a \\
  b \\
  c
  \end{pmatrix}
  =
  \begin{pmatrix}
  y_1 \\
  y_2 \\
  y_3
  \end{pmatrix}
  \]
   *Translation*: Prove that the coefficients \( a \), \( b \), and \( c \) are solutions of the linear system corresponding to the matrix.

### Question 8:
- The system of equations is:
  \[
  \begin{aligned}
  x + y + 2z &= a \\
  x + z &= b \\
  2x + y + 3z &= c
  \end{aligned}
  \]
  You are asked to show that for this system to be consistent, the constants \( a \), \( b \), and \( c \) must satisfy \( c = a + b \).

### Question 9:
- This question asks you to prove that if two linear equations \( x_1 + kx_2 = c \) and \( x_1 + lx_2 = d \) have the same solution set, then the two equations must be identical.

The image contains problems related to systems of linear equations and quadratic equations.

Explore detailed solutions for linear systems and quadratic equations using matrix algebra. This guide provides step-by-step explanations suitable for advanced high school and university mathematics students.

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