Question

2 aaliyah has regular chairs and 3-legged stools for a party. she has 9 seats all together which makes up 33 legs. which system of equations can be used to find the number of regular chairs, \\(c\\), and the number of stools, \\(s\\), she has?

f \\(\

$$\begin{aligned} c + s &= 33 \\\\ 4c + 3s &= 9 \\end{aligned}$$

\\)

g \\(\

$$\begin{aligned} c + s &= 9 \\\\ 4c + 3s &= 33 \\end{aligned}$$

\\)

h \\(\

$$\begin{aligned} c + s &= 33 \\\\ 4s + 3c &= 9 \\end{aligned}$$

\\)

j \\(\

$$\begin{aligned} c + s &= 9 \\\\ 4s + 3c &= 33 \\end{aligned}$$

\\)

Explanation:

Define variables and total seats

Using the Linear Function Modeling and Linear Equations knowledge points

$$
LATEXBLOCK0
$$

Model the total number of legs

Using the Linear Function Modeling and Linear Equations knowledge points

$$
LATEXBLOCK1
$$

Formulate the system of equations

Using the Linear Function Modeling and Linear Equations knowledge points

$$
LATEXBLOCK2
$$

Analyze the incorrect option F

Using the Linear Function Modeling and Linear Equations knowledge points

$$
LATEXBLOCK3
$$

Answer:

• F \(

$$\begin{cases} c + s = 33 \\ 4c + 3s = 9 \end{cases}$$

\)

• **G \(

$$\begin{cases} c + s = 9 \\ 4c + 3s = 33 \end{cases}$$

\) (Correct answer)**

• H \(

$$\begin{cases} c + s = 33 \\ 4s + 3c = 9 \end{cases}$$

\)

• J \(

$$\begin{cases} c + s = 9 \\ 4s + 3c = 33 \end{cases}$$

\)