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The given system of linear equations is:

\[
\begin{cases}
2x - 3y = 16 \\
-5x + y = -27
\end{cases}
\]

We will solve this system of equations using substitution or elimination.

### Step 1: Solve the second equation for \( y \):
\[
y = 5x - 27
\]

### Step 2: Substitute this expression for \( y \) into the first equation:
\[
2x - 3(5x - 27) = 16
\]
Simplify the equation:
\[
2x - 15x + 81 = 16
\]
\[
-13x + 81 = 16
\]
\[
-13x = 16 - 81
\]
\[
-13x = -65
\]
\[
x = \frac{-65}{-13} = 5
\]

### Step 3: Substitute \( x = 5 \) into the equation for \( y \):
\[
y = 5(5) - 27 = 25 - 27 = -2
\]

### Final Answer:
The values of \( x \) and \( y \) that satisfy both equations are:
\[
x = 5, \quad y = -2
\]

Would you like further details or clarification on any step? 

Here are 5 related questions to deepen your understanding:
1. What method would you prefer to use for solving linear systems, substitution or elimination?
2. How would the solution change if the constants in the equations were different?
3. Can a system of linear equations have no solution? Why?
4. What does it mean when two equations are dependent in a linear system?
5. How can you verify the solution by substituting back into both original equations?

**Tip:** Always check your solutions by plugging them back into the original equations to ensure they satisfy both.

Jika diberikan Sistem Persamaan linier 2x - 3y = 16 dan -5x + y = -27, maka nilai a dan b yang memenuhi kedua persamaan diatas adalah ....

Learn how to solve the system of linear equations 2x - 3y = 16 and -5x + y = -27 using substitution or elimination methods. This problem is suitable for students in Grades 9-12, focusing on algebraic methods to find the values of x and y.

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