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 3 3rd Column 4 2nd Row 1st Column 1 2nd Column 7 3rd Column 9 EndTable right bracket

6

3

4

1

7

9

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Part 1

Let 

x Subscript 1 

represent the variable for the first column and 

x Subscript 2

 represent the variable for the second column. 

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:

\[
\left[\begin{array}{ccc}
6 & 3 & 4 \\
1 & 7 & 9 \\
\end{array}\right]
\]

We assume the variables are \( x_1 \) and \( x_2 \). The augmented matrix represents the coefficients of the variables and the constants on the right-hand side of the equations. 

### The first row:
\[ 6x_1 + 3x_2 = 4 \]

### The second row:
\[ 1x_1 + 7x_2 = 9 \]

So, the system of linear equations is:

\[
\begin{aligned}
6x_1 + 3x_2 &= 4 \\
x_1 + 7x_2 &= 9
\end{aligned}
\]

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 linear equations using the substitution method?
2. How do you solve this system using the elimination method?
3. What does the solution of this system represent graphically?
4. How can this system of equations be represented as a vector equation?
5. What happens if the system of equations has no solution or infinite solutions?

**Tip:** Always double-check the coefficients and constants when translating from an augmented matrix to the system of equations to avoid errors.

Learn how to write a system of linear equations from an augmented matrix. Example problem with detailed explanation using variables x1 and x2. Suitable for high school students studying linear algebra.

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