Use Gauss-Jordan row reduction to solve the system of equations. $\begin{array} { l }
6 x + y = 12 \
6 x + 8 y = 5
\end{array}$
A) $\left( \frac { 13 } { 6 } , 1 \right)$
B) $\left( \frac { 13 } { 6 } , - 1 \right)$
C) $\left( \frac { 6 } { 13 } , 0 \right)$
D) $\left( \frac { 6 } { 13 } , 1 \right)$
E) $\left( \frac { 6 } { 13 } , - 1 \right)$

Question

Use Gauss-Jordan row reduction to solve the system of equations.   $\begin{array} { l } 
6 x + y = 12 \
6 x + 8 y = 5
\end{array}$  
A) $\left( \frac { 13 } { 6 } , 1 \right)$
B) $\left( \frac { 13 } { 6 } , - 1 \right)$
C) $\left( \frac { 6 } { 13 } , 0 \right)$
D) $\left( \frac { 6 } { 13 } , 1 \right)$
E)   $\left( \frac { 6 } { 13 } , - 1 \right)$

Quizplus · Accepted Answer

To solve the system using Gauss-Jordan row reduction, we first write the augmented matrix for the system:$$\begin{align*}\left[\begin{array}{cc|c}6 & 1 & 12 \6 & 8 & 5 \\end{array}\right]\end{align*}$$Next, we aim to make the matrix into reduced row echelon form (RREF). We can start by subtracting the first row from the second to eliminate $x$ from the second equation:$$\begin{align*}\left[\begin{array}{cc|c}6 & 1 & 12 \0 & 7 & -7 \\end{array}\right]\end{align*}$$Divide the second row by 7:$$\begin{align*}\left[\begin{array}{cc|c}6 & 1 & 12 \0 & 1 & -1 \\end{array}\right]\end{align*}$$Next, subtract the second row from the first row to eliminate $y$ from the first equation:$$\begin{align*}\left[\begin{array}{cc|c}6 & 0 & 13 \0 & 1 & -1 \\end{array}\right]\end{align*}$$Finally, divide the first row by 6:$$\begin{align*}\left[\begin{array}{cc|c}1 & 0 & \frac{13}{6} \0 & 1 & -1 \\end{array}\right]\end{align*}$$This gives us the solution $x = \frac{13}{6}$ and $y = -1$, which corresponds to choice B.

Use Gauss-Jordan Row Reduction to Solve the System of Equations 6x+y=126x+8y=5\begin{array} { l } 6 x + y = 12 \\6 x + 8 y = 5\end{array}6x+y=126x+8y=5​

Use Gauss-Jordan Row Reduction to Solve the System of Equations $\begin{array} { l } 6 x + y = 12 \\6 x + 8 y = 5\end{array}$