Question

question 37 points 3

the flower shop in a grocery store sells flowers individually. the relationship between \\(x\\), the cost on 1 rose, and \\(y\\), the cost of 1 carnation, is represented by the matrix equation. \\(\

$$\begin{bmatrix} 3 & 2 \\\\ 2 & 5 \\end{bmatrix}$$

\

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

= \

$$\begin{bmatrix} 8 \\\\ 9 \\end{bmatrix}$$

\\) find the cost of buying 1 rose.

\\(\bigcirc\\) $2.00

\\(\bigcirc\\) $0.82

Explanation:

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<reasoning>

Convert the matrix equation to a system of linear equations

Using the Matrix Multiplication and System of Linear Equations knowledge points
\[

$$\begin{aligned} &3x + 2y = 8 \\ &2x + 5y = 9 \end{aligned}$$

\]

Solve the system of equations for x

Using the Solving Matrix Equations knowledge point
\[

$$\begin{aligned} &5(3x + 2y) - 2(2x + 5y) = 5(8) - 2(9) \\ &15x + 10y - 4x - 10y = 40 - 18 \\ &11x = 22 \\ &x = 2 \end{aligned}$$

\]

Identify the cost of 1 rose

Using the Solving Matrix Equations knowledge point
\[
x = 2.00
\]
</reasoning>

<answer>
<mcq-correct>(A) $2.00</mcq-correct>
<mcq-option>(B) $0.82</mcq-option>
</answer>

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Answer:

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<reasoning>

Convert the matrix equation to a system of linear equations

Using the Matrix Multiplication and System of Linear Equations knowledge points
\[

$$\begin{aligned} &3x + 2y = 8 \\ &2x + 5y = 9 \end{aligned}$$

\]

Solve the system of equations for x

Using the Solving Matrix Equations knowledge point
\[

$$\begin{aligned} &5(3x + 2y) - 2(2x + 5y) = 5(8) - 2(9) \\ &15x + 10y - 4x - 10y = 40 - 18 \\ &11x = 22 \\ &x = 2 \end{aligned}$$

\]

Identify the cost of 1 rose

Using the Solving Matrix Equations knowledge point
\[
x = 2.00
\]
</reasoning>

<answer>
<mcq-correct>(A) $2.00</mcq-correct>
<mcq-option>(B) $0.82</mcq-option>
</answer>

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