Write the system of linear equations that is represented by the given augmented matrix. Assume that the variables are 

x Subscript 1 

and 

x Subscript 2.

left bracket Start 2 By 3 Table 1st Row 1st Column 6 2nd Column 0 3rd Column 4 2nd Row 1st Column 0 2nd Column 5 3rd Column 8 EndTable right bracket

6

0

4

0

5

8

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Part 1

The equation that represents the first row is 

enter your response here.

The equation that represents the second row is 

enter your response here.

​(Type equations using 

x 1x1 

and 

x 2x2 

as the variables. Type your answers in standard​ form.)

To write the system of linear equations represented by the given augmented matrix:

\[
\left[\begin{array}{ccc}
6 & 0 & 4 \\
0 & 5 & 8 \\
\end{array}\right]
\]

The variables \( x_1 \) and \( x_2 \) correspond to the first and second columns, respectively.

### The first row:
\[ 6x_1 + 0x_2 = 4 \]

This simplifies to:
\[ 6x_1 = 4 \]

### The second row:
\[ 0x_1 + 5x_2 = 8 \]

This simplifies to:
\[ 5x_2 = 8 \]

So, the system of linear equations is:

\[
\begin{aligned}
6x_1 &= 4 \\
5x_2 &= 8
\end{aligned}
\]

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. How do you solve this system of equations for \( x_1 \) and \( x_2 \)?
2. What are the solutions to the equations when expressed as fractions?
3. How would you verify the solutions to this system of equations?
4. How would the system change if the right-hand sides of the equations were different?
5. What is the graphical interpretation of this system of equations?

**Tip:** For systems with zeros in the matrix, it indicates that one of the variables does not appear in the corresponding equation, simplifying the solving process.

Understand how to write a system of linear equations from an augmented matrix [6 0 4; 0 5 8]. Learn the standard form of linear equations using variables x₁ and x₂. Suitable for Grades 9-12.

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