Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { r }
3 x + 5 y = - 10 \
- 3 x - 6 y = 9
\end{array}$$
A) $\{ ( - 5,1 ) \}$
B) $\{ ( 5 , - 1 ) \}$
C) $\{ ( - 1,5 ) \}$
D) $\{ ( 1 , - 5 ) \}$

Question

Solve the system by using the inverse of the coefficient matrix.
-$$\begin{array} { r } 
3 x + 5 y = - 10 \
- 3 x - 6 y = 9
\end{array}$$
A) $\{ ( - 5,1 ) \}$
B) $\{ ( 5 , - 1 ) \}$
C) $\{ ( - 1,5 ) \}$
D) $\{ ( 1 , - 5 ) \}$

Quizplus · Accepted Answer

To solve the system using the inverse of the coefficient matrix, first write the system in matrix form as AX = B, where A is the coefficient matrix, X is the column matrix of variables, and B is the column matrix of constants. For this system, $$A = \begin{pmatrix} 3 & 5 \ -3 & -6 \end{pmatrix}, X = \begin{pmatrix} x \ y \end{pmatrix}, B = \begin{pmatrix} -10 \ 9 \end{pmatrix}$$. To find X, compute X = A^{-1}B. The inverse of A, A^{-1}, can be found using the formula for the inverse of a 2x2 matrix. After finding A^{-1}, multiply it by B to get X. The solution corresponds to choice A, $\{ ( - 5,1 ) \}$.

Solve the System by Using the Inverse of the Coefficient 3x+5y=−10−3x−6y=9\begin{array} { r } 3 x + 5 y = - 10 \\- 3 x - 6 y = 9\end{array}3x+5y=−10−3x−6y=9​

Solve the System by Using the Inverse of the Coefficient $\begin{array} { r } 3 x + 5 y = - 10 \\- 3 x - 6 y = 9\end{array}$