Solve the system of equations by using the inverse of the coefficient matrix if it exists and by the echelon method if the
inverse doesn't exist.
-$$
\begin{array}{l}
-3 x+9 y=9 \
3 x+2 y=13
\end{array}
$$
A) $ (3,2) $
B) $ (-3,-2) $
C) $ (-2,-3) $
D) $ (2,3) $

Question

Quizplus · Accepted Answer

The coefficient matrix of the system is $\begin{pmatrix} -3 & 9 \ 3 & 2 \end{pmatrix}$, and the constant matrix is $\begin{pmatrix} 9 \ 13 \end{pmatrix}$. The determinant of the coefficient matrix is $(-3)(2) - (9)(3) = -6 - 27 = -33$, which is not zero, so the inverse exists. Solving the system using either method will yield the solution $x = 3, y = 2$, which corresponds to choice A.

Solve the System of Equations by Using the Inverse of the Coefficient