Question

1. the pet kennel is boarding a total of 12 dogs and cats for the weekend. the number of dogs is three less than twice the number of cats. which system of linear equations models this scenario? for this scenario, let ( d = ) the number of dogs and let ( c = ) the number of cats. ( \bigcirc \begin{cases} d + c = 12 \\ d = 2c - 3 end{cases} ) ( \bigcirc \begin{cases} d + c = 12 \\ 2c = d - 3 end{cases} ) ( \bigcirc \begin{cases} d + c = 12 \\ d = 3 - 2c end{cases} ) ( \bigcirc \begin{cases} d + c = 12 \\ c = 2d - 3 end{cases} )

Explanation:

Step1: Analyze total number equation

The total number of dogs (\(d\)) and cats (\(c\)) is 12, so \(d + c = 12\).

Step2: Analyze dogs - cats relationship

The number of dogs is three less than twice the number of cats. Twice the number of cats is \(2c\), three less than that is \(2c - 3\), so \(d = 2c - 3\).

Step3: Match with options

The first option has \(d + c = 12\) and \(d = 2c - 3\), which matches our deductions.

Answer:

$$\begin{cases} d + c = 12 \\ d = 2c - 3 \end{cases}$$

(the first option: $\boldsymbol{

$$\begin{cases} d + c = 12 \\ d = 2c - 3 \end{cases}$$

}$)