Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations.
-$$\begin{array} { l }
9 x + y = 32 \
9 x + y = 59
\end{array}$$
A) system is inconsistent
B) system contains dependent equations

Question

Use Cramer's rule to determine if the system is inconsistent system or contains dependent equations.
-$$\begin{array} { l } 
9 x + y = 32 \
9 x + y = 59
\end{array}$$
A) system is inconsistent
B) system contains dependent equations

Quizplus · Accepted Answer

To use Cramer's rule, we need to find the determinant of the coefficient matrix and the determinant of the matrix formed by replacing the first column with the constants. The coefficient matrix is $\begin{pmatrix}9 & 1 \9 & 1\end{pmatrix}$ and its determinant is $9(1)-1(9)=0$. The matrix formed by replacing the first column with the constants is $\begin{pmatrix}32 & 1 \59 & 1\end{pmatrix}$ and its determinant is $32(1)-1(59)=-27$. Since the determinant of the coefficient matrix is $0$, the system is inconsistent.

Use Cramer's Rule to Determine If the System Is Inconsistent 9x+y=329x+y=59\begin{array} { l } 9 x + y = 32 \\9 x + y = 59\end{array}9x+y=329x+y=59​

Use Cramer's Rule to Determine If the System Is Inconsistent $\begin{array} { l } 9 x + y = 32 \\9 x + y = 59\end{array}$