Answer :
To write the augmented matrix for the given system of equations, we need to start by identifying the coefficients and constants from each of the equations.
We have the following system of equations:
[tex]\[ \begin{array}{l} 10x = 10 \\ -5x - 8y = 9 \end{array} \][/tex]
### Step-by-Step Solution:
1. Extract the Coefficients and Constants:
From the first equation:
[tex]\[ 10x = 10 \][/tex]
The coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and the constant term are:
[tex]\[ [10, 0, 10] \][/tex]
Here, there is no [tex]\(y\)[/tex] term, so its coefficient is 0.
From the second equation:
[tex]\[ -5x - 8y = 9 \][/tex]
The coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and the constant term are:
[tex]\[ [-5, -8, 9] \][/tex]
2. Formulate the Augmented Matrix:
The augmented matrix is constructed by placing the coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from each equation and the constants as the final column.
Thus, the augmented matrix for the system of equations is:
[tex]\[ \begin{bmatrix} 10 & 0 & 10 \\ -5 & -8 & 9 \end{bmatrix} \][/tex]
So, the augmented matrix is:
[tex]\[ \begin{bmatrix} 10 & 0 & 10 \\ -5 & -8 & 9 \end{bmatrix} \][/tex]
We have the following system of equations:
[tex]\[ \begin{array}{l} 10x = 10 \\ -5x - 8y = 9 \end{array} \][/tex]
### Step-by-Step Solution:
1. Extract the Coefficients and Constants:
From the first equation:
[tex]\[ 10x = 10 \][/tex]
The coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and the constant term are:
[tex]\[ [10, 0, 10] \][/tex]
Here, there is no [tex]\(y\)[/tex] term, so its coefficient is 0.
From the second equation:
[tex]\[ -5x - 8y = 9 \][/tex]
The coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex], and the constant term are:
[tex]\[ [-5, -8, 9] \][/tex]
2. Formulate the Augmented Matrix:
The augmented matrix is constructed by placing the coefficients of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] from each equation and the constants as the final column.
Thus, the augmented matrix for the system of equations is:
[tex]\[ \begin{bmatrix} 10 & 0 & 10 \\ -5 & -8 & 9 \end{bmatrix} \][/tex]
So, the augmented matrix is:
[tex]\[ \begin{bmatrix} 10 & 0 & 10 \\ -5 & -8 & 9 \end{bmatrix} \][/tex]
