Questions: Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.) 2x+3y=-5 x+3y=-7 x-y=3 (x, y)=

Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTION. If there are infinitely many solutions, express your answer in terms of the parameters t and/or s.)
2x+3y=-5
x+3y=-7
x-y=3
(x, y)=

Transcript text: Solve the system of linear equations, using the Gauss-Jordan elimination method. (If there is no solution, enter NO SOLUTioN. If there are infinitely many solutions, express your answer in terms of the parameters $t$ and/or s.) \[ \begin{array}{r} 2 x+3 y=-5 \\ x+3 y=-7 \\ x-y=3 \\ (x, y)=\square \end{array} \]

Solution

Solution Steps

To solve the system of linear equations using the Gauss-Jordan elimination method, we will:

Represent the system of equations as an augmented matrix.
Perform row operations to transform the matrix into reduced row echelon form (RREF).
Interpret the resulting matrix to find the values of $x$ and $y$.

Step 1: Represent the System of Equations as an Augmented Matrix

We start by representing the given system of linear equations as an augmented matrix: \[ \begin{bmatrix} 2 & 3 & -5 \\ 1 & 3 & -7 \\ 1 & -1 & 3 \end{bmatrix} \]

Step 2: Apply Gauss-Jordan Elimination

We perform row operations to transform the augmented matrix into its reduced row echelon form (RREF). The resulting matrix is: \[ \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \]

Step 3: Interpret the RREF Matrix

The RREF matrix indicates that: \[ \begin{cases} x = 0 \\ y = 0 \end{cases} \]