Question

Write an augmented matrix and use elementary row operations in order to solve the following system of equations. Your final matrix should be in reduced row echelon form. In order to get credit you will have to have a correct final answer as accurate steps in each row operation.

-3x+5=3
-2x+5y=-8

Answer 1

x=8, y=-1

Explanation:

Given: -3x+5=3 -2x+5y=-8 Augmented Matrix: \begin{bmatrix} -3 & 5 & 3 \\ -2 & 5 & -8 \end{bmatrix} Chain of Thought: \begin{bmatrix} -3 & 5 & 3 \\ -2 & 5 & -8 \end{bmatrix} Row 1) \begin{bmatrix} -3 & 5 & 3 \\ 0 & 5 & -5 \end{bmatrix} Steps: Add row 1 to row 2 \begin{bmatrix} 1 & 0 & 8\\ 0 & 5 & -5 \end{bmatrix} Row 2) \begin{bmatrix} 1 & 0 & 8\\ 0 & 5 & -5 \end{bmatrix} Steps: Divide row 2 by 5 \begin{bmatrix} 1 & 0 & 8\\ 0 & 1 & -1 \end{bmatrix} Solution Matrix: \begin{bmatrix} 1 & 0 & 8\\ 0 & 1 & -1 \end{bmatrix} Answer: x=8, y=-1