Solve the linear system using an inverse matrix.
-$$\begin{array} { l }
- 3 x + 9 y = 9 \
3 x + 2 y = 13
\end{array}$$
A) $( 3,2 )$
B) $( - 3 , - 2 )$
C) $( 2,3 )$
D) $( - 2 , - 3 )$

Question

Solve the linear system using an inverse matrix.
-$$\begin{array} { l } 
- 3 x + 9 y = 9 \
3 x + 2 y = 13
\end{array}$$
A) $( 3,2 )$
B) $( - 3 , - 2 )$
C) $( 2,3 )$
D) $( - 2 , - 3 )$

Quizplus · Accepted Answer

To solve the system using an inverse 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 solutions. For this system, A = $\begin{pmatrix} -3 & 9 \ 3 & 2 \end{pmatrix}$, X = $\begin{pmatrix} x \ y \end{pmatrix}$, and B = $\begin{pmatrix} 9 \ 13 \end{pmatrix}$. The solution is given by X = A^{-1}B. Calculating the inverse of A and multiplying it by B gives the solution X = $\begin{pmatrix} 3 \ 2 \end{pmatrix}$, which corresponds to the point (3, 2).

Solve the Linear System Using an Inverse Matrix −3x+9y=93x+2y=13\begin{array} { l } - 3 x + 9 y = 9 \\3 x + 2 y = 13\end{array}−3x+9y=93x+2y=13​

Solve the Linear System Using an Inverse Matrix $\begin{array} { l } - 3 x + 9 y = 9 \\3 x + 2 y = 13\end{array}$