A test is worth 100 points. The test is made up of 40 items. Each item is worth either 2 points or 3 points. Which matrix equation and solution represent the situation?

Answer:Total number of points in the test = 100Total number of items in the test = 40Let number of items of 2 points be x and number of items of 3 points be y.Now, using the given information the situation can be represented by using the following equations :⇒ x + y = 40 .........(1)⇒ 2x + 3y = 100 .........(2)The matrix equation is :[tex]\begin{bmatrix}1 & 1\\ 2& 3\end{bmatrix}\cdot \begin{bmatrix}x\\ y\end{bmatrix}=\begin{bmatrix}40\\ 100\end{bmatrix}[/tex]By solving the equation (1) and equation (2), we get :Solution : x = 20 and y = 20