Question

question 28 points 2

heather bought two sizes of ceramic tiles. each size was a different price. the matrix equation \\(\

$$\begin{bmatrix} 1 & 1 \\\\ 1 & 2 \\end{bmatrix}$$

\

$$\begin{bmatrix} x \\\\ y \\end{bmatrix}$$

= \

$$\begin{bmatrix} 50 \\\\ 80 \\end{bmatrix}$$

\\) can be used to solve the number of small tiles (x) and large tiles (y). how many small tiles did she buy?

25

20

Explanation:

Set up the system of equations

Using the Solving Matrix Equations knowledge point

$$
LATEXBLOCK0
$$

Solve for the variables

Subtract the first equation from the second equation to eliminate \(x\):

$$ (1x + 2y) - (1x + 1y) = 80 - 50 $$

$$ y = 30 $$

Substitute \(y = 30\) back into the first equation to find \(x\):

$$ x + 30 = 50 $$

$$ x = 20 $$

Identify the target value

The variable \(x\) represents the number of small tiles.

$$ x = 20 $$

Answer:

• 25
• 20 (Correct answer)