Write System of Linear Equations from Augmented Matrix

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

Question content area bottom

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:

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.

Drop file here or Click Here to upload

Linear Equations
Augmented Matrix
Systems of Equations

Standard form of linear equations

Grades 9-12

System of Linear Equations from Augmented Matrix [3 -7 0 2; 8 6 -2 0; -7 0 4 3]

Solve a System of Equations from an Augmented Matrix

Writing Systems of Equations from an Augmented Matrix

Matrix Representation of Systems of Linear Equations - Example with Augmented Matrix

Augmented Matrix for System of Linear Equations