System of Linear Equations from Augmented Matrix [6 0 4; 0 5 8]

Math Problem Statement

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

Question content area bottom

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:

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.

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Linear Equations
Augmented Matrix

Standard form of linear equations

Grades 9-12

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