Question

1. the pet kennel has 12 dogs and cats for the weekend. the number of dogs is three less than twice the number of cats. write a system of equations to model this.\\(\

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

\\)\\(\

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

\\)\\(\

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

\\)\\(\

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

\\)

Explanation:

Step1: Define total pets equation

Let $d$ = number of dogs, $c$ = number of cats. Total pets: $d + c = 12$

Step2: Define dog-cat relationship equation

Dogs = 2×cats - 3: $d = 2c - 3$

Step3: Match to option

Pair equations into a system:

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

Answer:

$\boldsymbol{

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

}$ (the fourth option)