Convert a system of equations into an augmented matrix - High school Algebra II Exercises

Determine the augmented matrix associated with the following systems of linear equations.

\begin{cases} 2x-y=4 \cr \cr 4x+2y=3 \end{cases}

\begin{pmatrix} 12 & -4 & 2 \cr\cr 2 & 4 & 3 \end{pmatrix}

\begin{pmatrix} -2 & 1 & -4 \cr\cr 4 & 2 & 3 \end{pmatrix}

\begin{pmatrix} 2 & -1 & 4 \cr\cr 4 & 2 & 3 \end{pmatrix}

\begin{pmatrix} 2 & -1 & 4 \cr\cr -4 & -2 & -3 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} 2x-y=4 \cr \cr 4x+2y=3 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{2}x-\textcolor{Red}{1}y=\textcolor{Red}{4} \cr \cr \textcolor{Red}{4x}+\textcolor{Red}{2}y=\textcolor{Red}{3}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} 2 & -1 & 4 \cr\cr 4 & 2 & 3 \end{pmatrix}.

\begin{cases} 4x+2y=7 \cr \cr 2x+y=5 \end{cases}

\begin{pmatrix} 5 & 3 & 2 \cr\cr -3 & -1 & 2 \end{pmatrix}

\begin{pmatrix} 4 & 1 & 12 \cr\cr 3 & 1 & -2 \end{pmatrix}

\begin{pmatrix} 4 & 2 & 7 \cr\cr 2 & 1 & 5 \end{pmatrix}

\begin{pmatrix} 1 & -3 & 2 \cr\cr 2 & 6 & -2 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} 4x+2y=7 \cr \cr 2x+y=5 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{4}x+\textcolor{Red}{2}y=\textcolor{Red}{7} \cr \cr \textcolor{Red}{2x}+\textcolor{Red}{1}y=\textcolor{Red}{5}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} 4 & 2 & 7 \cr\cr 2 & 1 & 5 \end{pmatrix}.

\begin{cases} 3x-2y=2 \cr \cr x+3y=-3 \end{cases}

\begin{pmatrix} 3 & 4 & 2 \cr\cr 3 & 1 & 2 \end{pmatrix}

\begin{pmatrix} 3 & -2 & 2 \cr\cr 1 & 3 & -3 \end{pmatrix}

\begin{pmatrix} 3 & 1 & -3 \cr\cr 5 & 3 & 3 \end{pmatrix}

\begin{pmatrix} 1 & 2 & -2 \cr\cr 5 & -3 & 3 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} 3x-2y=2 \cr \cr x+3y=-3 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{3}x+\left(\textcolor{Red}{-2}y\right)=\textcolor{Red}{2} \cr \cr \textcolor{Red}{1x}+\textcolor{Red}{3}y=\textcolor{Red}{-3}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} 3 & -2 & 2 \cr\cr 1 & 3 & -3 \end{pmatrix}.

\begin{cases} 5x-2y=-1 \cr \cr 4x+6y=-1 \end{cases}

\begin{pmatrix} 5 & -2 & 1 \cr\cr 4 & 6 & 1 \end{pmatrix}

\begin{pmatrix} 5 & 2 & 1 \cr\cr 4 & 6 & 1 \end{pmatrix}

\begin{pmatrix} 5 & -2 & -1 \cr\cr 4 & 6 & -1 \end{pmatrix}

\begin{pmatrix} 5 & 2 & -1 \cr\cr 4 & 6 & -1 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} 5x-2y=-1 \cr \cr 4x+6y=-1 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{5}x+\left(\textcolor{Red}{-2}y\right)=\textcolor{Red}{-1} \cr \cr \textcolor{Red}{4x}+\textcolor{Red}{6}y=\textcolor{Red}{-1}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} 5 & -2 & -1 \cr\cr 4 & 6 & -1 \end{pmatrix}.

\begin{cases} -1x-y=-4 \cr \cr -4x+5y=-9 \end{cases}

\begin{pmatrix} -1 & 1 & 4 \cr\cr 4 & 5 & -9 \end{pmatrix}

\begin{pmatrix} -1 & -1 & 4 \cr\cr 4 & 5 & 9 \end{pmatrix}

\begin{pmatrix} -1 & -1 & -4 \cr\cr -4 & 5 & -9 \end{pmatrix}

\begin{pmatrix} 1 & 1 & 4 \cr\cr 4 & 5 & 9 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} -1x-y=-4 \cr \cr -4x+5y=-9 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{-1}x+\left(\textcolor{Red}{-1}y\right)=\textcolor{Red}{-4} \cr \cr \textcolor{Red}{-4x}+\textcolor{Red}{5}y=\textcolor{Red}{-9}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} -1 & -1 & -4 \cr\cr -4 & 5 & -9 \end{pmatrix}.

\begin{cases} 2x=-4 \cr \cr -2y=9 \end{cases}

\begin{pmatrix} -2 & & -4 \cr\cr & -2 & 9 \end{pmatrix}

\begin{pmatrix} 2 & & 4 \cr\cr & 2 & 9 \end{pmatrix}

\begin{pmatrix} 2 & 0 & 4 \cr\cr 0 & 2 & 9 \end{pmatrix}

\begin{pmatrix} 2 & 0 & -4 \cr\cr 0 & -2 & 9 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} 2x=-4 \cr \cr -2y=9 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{2}x+\textcolor{Red}{0}y=\textcolor{Red}{-4} \cr \cr \textcolor{Red}{0x}+\left(\textcolor{Red}{-2}y\right)=\textcolor{Red}{9}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} 2 & 0 & -4 \cr\cr 0 & -2 & 9 \end{pmatrix}.

\begin{cases} 21x-12y=43 \cr \cr 14x+42y=23 \end{cases}

\begin{pmatrix} 21 & 12 & 43 \cr\cr 14 & 42 & -23 \end{pmatrix}

\begin{pmatrix} 21 & 12 & 43 \cr\cr 14 & 42 & 23 \end{pmatrix}

\begin{pmatrix} 21 & -12 & 43 \cr\cr 14 & 42 & 23 \end{pmatrix}

\begin{pmatrix} 21 & -2 & 43 \cr\cr 14 & -42 & 23 \end{pmatrix}

In order to convert a system of linear equations into an augmented matrix, we take the coefficients of the system and place them in a matrix.

Here we have:

\begin{cases} 21x-12y=43 \cr \cr 14x+42y=23 \end{cases}

The coefficients are:

\begin{cases} \textcolor{Red}{21}x+\left(\textcolor{Red}{-12}y\right)=\textcolor{Red}{43} \cr \cr \textcolor{Red}{14x}+\textcolor{Red}{42}y=\textcolor{Red}2{3}\end{cases}

The augmented matrix associated with this system is \begin{pmatrix} 21 & -12 & 43 \cr\cr 14 & 42 & 23 \end{pmatrix}.