Solve the system using the inverse matrix method.
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A)x = 2, y = 6; (2, 6)
B)x = 6, y = 2; (6, 2)
C)x = -2, y = -6; (-2, -6)
D)x = -6, y = -2; (-6, -2)

Question

Solve the system using the inverse matrix method.
-
A)x = 2, y = 6; (2, 6) 
B)x = 6, y = 2; (6, 2) 
C)x = -2, y = -6; (-2, -6) 
D)x = -6, y = -2; (-6, -2)

Quizplus · Accepted Answer

Using the inverse matrix method, we get:
$$
\begin{bmatrix}
5 & 1 \
2 & 4
\end{bmatrix}^{-1}
\begin{bmatrix}
7 \ 23
\end{bmatrix}
= 
\begin{bmatrix}
2 \ 6
\end{bmatrix}
$$
Therefore, the solution is (2, 6), which corresponds to choice A. Using the inverse matrix method:
First find the inverse of the coefficient matrix:
| 4 1 |^-1 = (1/43)| -5 4 |
                      | 11 -4 |
Then multiply it by the constant matrix:
(1/43)| -5 4 | * | 29 | = | 2 |
          | 11 -4 |      | 6 |
So the solution is (2,6).

Solve the System Using the Inverse Matrix Method