Solve using matrices.
-$\begin{array} { l }
2 x + y = 6 \
9 x + 2 y = 37
\end{array}$

A) $( - 4 , - 5 )$
B) $( 5 , - 5 )$
C) $( 5 , - 4 )$
D) $( - 4,5 )$

Question

Solve using matrices.
-$\begin{array} { l } 
2 x + y = 6 \
9 x + 2 y = 37
\end{array}$

A) $( - 4 , - 5 )$
B) $( 5 , - 5 )$
C) $( 5 , - 4 )$
D) $( - 4,5 )$

Quizplus · Accepted Answer

We can write the given system of equations in matrix form as:
$\begin{bmatrix} 2 & 1 \ 9 & 2 \end{bmatrix} \begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 6 \ 37 \end{bmatrix}$

To solve for $\begin{bmatrix} x \ y \end{bmatrix}$, we can left-multiply both sides by the inverse of the coefficient matrix:
$\begin{bmatrix} x \ y \end{bmatrix} = \begin{bmatrix} 2 & 1 \ 9 & 2 \end{bmatrix}^{-1} \begin{bmatrix} 6 \ 37 \end{bmatrix}$

Using row reduction (or a calculator), we can find that the inverse of the coefficient matrix is:
$\begin{bmatrix} 2 & -1 \ -9 & 2 \end{bmatrix}^{-1} = \frac{1}{16} \begin{bmatrix} 2 & 1 \ 9 & 2 \end{bmatrix}$

Substituting this into the equation above, we get:
$\begin{bmatrix} x \ y \end{bmatrix} = \frac{1}{16} \begin{bmatrix} 2 & 1 \ 9 & 2 \end{bmatrix} \begin{bmatrix} 6 \ 37 \end{bmatrix} = \begin{bmatrix} 5 \ -4 \end{bmatrix}$

Therefore, the solution is $(x,y) = \boxed{(5,-4)}$.

Solve Using Matrices 2x+y=69x+2y=37\begin{array} { l } 2 x + y = 6 \\9 x + 2 y = 37\end{array}2x+y=69x+2y=37​

Solve Using Matrices $\begin{array} { l } 2 x + y = 6 \\9 x + 2 y = 37\end{array}$