Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\left\{ \begin{array} { l }
5 x + 6 y = 20 \
2 x + 8 y = 36
\end{array} \right.$$
A) $x = - 2 , y = - 5$
B) $x = 5 , y = - 2$
C) $x = - 2 , y = 5$
D) Inconsistent

Question

Solve each system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent.
-$$\left\{ \begin{array} { l } 
5 x + 6 y = 20 \
2 x + 8 y = 36
\end{array} \right.$$
A) $x = - 2 , y = - 5$
B) $x = 5 , y = - 2$
C) $x = - 2 , y = 5$
D) Inconsistent

Quizplus · Accepted Answer

To solve the system using matrices, we first write the augmented matrix for the system, then perform row operations to get it into reduced row echelon form (RREF).The augmented matrix is:$$\begin{bmatrix}5 & 6 & | & 20 \2 & 8 & | & 36 \\end{bmatrix}$$Step 1: Make the leading coefficient of the first row 1 (optional since it's already easy to work with).Step 2: Eliminate the x-term from the second row. We can multiply the first row by 2 and subtract it from the second row multiplied by 5 to eliminate x from the second row.$$\begin{bmatrix}5 & 6 & | & 20 \0 & 20 & | & 60 \\end{bmatrix}$$Step 3: Simplify the second row by dividing it by 20.$$\begin{bmatrix}5 & 6 & | & 20 \0 & 1 & | & 3 \\end{bmatrix}$$Step 4: Eliminate the y-term from the first row. We can multiply the second row by 6 and subtract it from the first row.$$\begin{bmatrix}5 & 0 & | & -2 \0 & 1 & | & 3 \\end{bmatrix}$$Step 5: Simplify the first row by dividing it by 5.$$\begin{bmatrix}1 & 0 & | & -2 \0 & 1 & | & 3 \\end{bmatrix}$$This gives us the solution $x = -2, y = 5$.

Solve Each System of Equations Using Matrices (Row Operations) {5x+6y=202x+8y=36\left\{ \begin{array} { l } 5 x + 6 y = 20 \\2 x + 8 y = 36\end{array} \right.{5x+6y=202x+8y=36​

Solve Each System of Equations Using Matrices (Row Operations) $\left\{ \begin{array} { l } 5 x + 6 y = 20 \\2 x + 8 y = 36\end{array} \right.$