Use the Gauss-Jordan method to solve the system of equations.
-$$
\begin{array}{l}
6 x+5 y=0 \
3 x+9 y=39
\end{array}
$$
A) $ (-5,-6) $
B) $ (6,-5) $
C) $ (-5,6) $
D) No solution

Question

Quizplus · Accepted Answer

The Gauss-Jordan method involves transforming the system of equations into reduced row echelon form. Starting with the system:1. $6x + 5y = 0$2. $3x + 9y = 39$First, we can divide the first equation by 3 to simplify:1. $2x + \frac{5}{3}y = 0$2. $3x + 9y = 39$Next, we can eliminate $x$ from the second equation by subtracting $3/2$ times the first equation from the second:1. $2x + \frac{5}{3}y = 0$2. $0x + \frac{17}{3}y = 39$Solving the second equation for $y$ gives $y = \frac{39}{\frac{17}{3}} = \frac{39 \cdot 3}{17} = 6.9$, which simplifies to $y = 6$.Substituting $y = 6$ into the first equation:$2x + \frac{5}{3}(6) = 0$$2x + 10 = 0$$2x = -10$$x = -5$Therefore, the solution is $(-5, 6)$.

Use the Gauss-Jordan Method to Solve the System of Equations 6x+5y=03x+9y=39\begin{array}{l}6 x+5 y=0 \\3 x+9 y=39\end{array}6x+5y=03x+9y=39​

Use the Gauss-Jordan Method to Solve the System of Equations $\begin{array}{l}6 x+5 y=0 \\3 x+9 y=39\end{array}$