Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$\left\{ \begin{array} { l }
2 x + 6 y = 10 \
2 x + 3 y = 7
\end{array} \right.$$
A) (10, 1)
B) (2, 1)
C) (2, -6)
D) (-2, 1)
E) (2, -1)

Question

Use matrices to solve the system of equations (if possible).Use Gaussian elimination with back-substitution or Gauss-Jordan elimination.   $$\left\{ \begin{array} { l } 
2 x + 6 y = 10 \
2 x + 3 y = 7
\end{array} \right.$$  
A) (10, 1)
B) (2, 1)
C) (2, -6)
D) (-2, 1)
E) (2, -1)

Quizplus · Accepted Answer

To solve the system of equations using matrices, we can write the augmented matrix and apply Gaussian elimination or Gauss-Jordan elimination. The augmented matrix for the system is:$$\begin{align*}\left[\begin{array}{cc|c}2 & 6 & 10 \2 & 3 & 7 \\end{array}\right]\end{align*}$$First, we can subtract the second row from the first to eliminate $x$ from the first equation:$$\begin{align*}\left[\begin{array}{cc|c}0 & 3 & 3 \2 & 3 & 7 \\end{array}\right]\end{align*}$$Then, we can divide the first row by 3 to get the coefficient of $y$ to 1:$$\begin{align*}\left[\begin{array}{cc|c}0 & 1 & 1 \2 & 3 & 7 \\end{array}\right]\end{align*}$$Next, we can use the first row to eliminate $y$ from the second equation by subtracting 3 times the first row from the second row:$$\begin{align*}\left[\begin{array}{cc|c}0 & 1 & 1 \2 & 0 & 4 \\end{array}\right]\end{align*}$$Finally, divide the second row by 2 to get the coefficient of $x$ to 1:$$\begin{align*}\left[\begin{array}{cc|c}0 & 1 & 1 \1 & 0 & 2 \\end{array}\right]\end{align*}$$This gives us the solutions $y = 1$ and $x = 2$, which corresponds to choice (B) (2, 1).

Use Matrices to Solve the System of Equations (If Possible) {2x+6y=102x+3y=7\left\{ \begin{array} { l } 2 x + 6 y = 10 \\2 x + 3 y = 7\end{array} \right.{2x+6y=102x+3y=7​

Use Matrices to Solve the System of Equations (If Possible) $\left\{ \begin{array} { l } 2 x + 6 y = 10 \\2 x + 3 y = 7\end{array} \right.$