CPM Homework Help : PC3 Problem 9-86

Juanita wants to solve the following problem using matrices, but is not sure how.

The cost of two pencils, two pens, and two erasers is $$2.46$ . The cost of two pencils, five pens, and one eraser is $$4.38$ . The cost of one pencil, one pen, and two erasers is $$1.38$ . What is the cost of each item?

Explain what she should do.
Hint (a):
Think about how you would write an equation for each sentence.
What would your system of equations look like?
How could you write your system as a matrix equation instead?

Solve this problem.
Step (b):
$\begin{bmatrix}2&2&2\\2&5&1\\1&1&2\end{bmatrix}\begin{bmatrix}x\\y\\z\end{bmatrix}=\begin{bmatrix}2.46\\4.38\\1.38\end{bmatrix}$
$\text{Where }x = \text{cost of } 1 \text{ pencil}, y = \text{cost of } 1 \text{ pen}, z = \text{ cost of } 1 \text{ eraser.}$
Solve for $x, y,$ and $z$ using a calculator.