Question

question 7 of 10, step 1 of 1
use gauss-jordan elimination to solve the following system of equations. if there is a solution, write your answer in the format (x, y).
\

$$\begin{cases}7x + 4y = -58\\\\4x + 3y = -36\\end{cases}$$

indicate the number of solutions to this system. state the solution, if one exists, and if there are infinitely many solutions, express the solution set in terms of one of the variables.
selecting an option will display any text boxes needed to complete your answer.
\bigcirc no solution
\bigcirc one solution
\bigcirc infinitely many solutions

Explanation:

Step1: Write augmented matrix

$$\begin{bmatrix} 7 & 4 & \mid & -58 \\ 4 & 3 & \mid & -36 \end{bmatrix}$$

Step2: Normalize row1 (divide by 7)

$$\begin{bmatrix} 1 & \frac{4}{7} & \mid & -\frac{58}{7} \\ 4 & 3 & \mid & -36 \end{bmatrix}$$

Step3: Eliminate x from row2

Row2 = Row2 - 4×Row1

$$\begin{bmatrix} 1 & \frac{4}{7} & \mid & -\frac{58}{7} \\ 0 & \frac{5}{7} & \mid & -\frac{20}{7} \end{bmatrix}$$

Step4: Normalize row2 (multiply by $\frac{7}{5}$)

$$\begin{bmatrix} 1 & \frac{4}{7} & \mid & -\frac{58}{7} \\ 0 & 1 & \mid & -4 \end{bmatrix}$$

Step5: Eliminate y from row1

Row1 = Row1 - $\frac{4}{7}$×Row2

$$\begin{bmatrix} 1 & 0 & \mid & -6 \\ 0 & 1 & \mid & -4 \end{bmatrix}$$

Answer:

○ One Solution
$(-6, -4)$