melissa made a total of 14 baskets during her last basketball game. she made a number of 2 - point baskets…

Explanation:

Step1: Set up equations

Let $x$ be the number of 2 - point baskets and $y$ be the number of 3 - point baskets. We have the system of equations: $\begin{cases}x + y=14\2x + 3y=33\end{cases}$. In matrix form $AX = B$, where $A=\begin{bmatrix}1&1\2&3\end{bmatrix}$, $X=\begin{bmatrix}x\y\end{bmatrix}$ and $B=\begin{bmatrix}14\33\end{bmatrix}$.

Step2: Find the inverse of matrix $A$

The determinant of $A$, $\text{det}(A)=1\times3 - 1\times2=1$. The inverse of $A$, $A^{-1}=\begin{bmatrix}3&- 1\-2&1\end{bmatrix}$.

Step3: Solve for $X$

$X = A^{-1}B=\begin{bmatrix}3&-1\-2&1\end{bmatrix}\begin{bmatrix}14\33\end{bmatrix}=\begin{bmatrix}3\times14+( - 1)\times33\-2\times14 + 1\times33\end{bmatrix}=\begin{bmatrix}42-33\-28 + 33\end{bmatrix}=\begin{bmatrix}9\5\end{bmatrix}$.

Answer:

B. 5