Question

6.2 unit 7 test
semiras puppy weighs 12.4 pounds and is growing at a rate of 0.8 pounds per week. cedrics puppy weighs 9.2 pounds and is growing at a rate of 1.2 pounds per week. let x represent the time in weeks and y represent the weight of the puppy in pounds. which system of equations can semira and cedric use to determine after how many weeks their puppies will weigh the same?
$\

$$\begin{cases} y = 0.8x + 12.4 \\\\ y = 1.2x + 9.2 \\end{cases}$$

$
$\

$$\begin{cases} y = 1.2x + 0.8 \\\\ y = 9.2x + 1.2 \\end{cases}$$

$
$\

$$\begin{cases} y = 0.8x + 1.2 \\\\ y = 12.4x + 9.2 \\end{cases}$$

$
$\

$$\begin{cases} y = 1.2x + 0.8 \\\\ y = 9.2x + 12.4 \\end{cases}$$

$

Explanation:

Step1: Define Semira's puppy weight equation

The weight follows the form $y = \text{growth rate} \times x + \text{initial weight}$. For Semira's puppy, growth rate is $0.8$ and initial weight is $12.4$, so:
$y = 0.8x + 12.4$

Step2: Define Cedric's puppy weight equation

For Cedric's puppy, growth rate is $1.2$ and initial weight is $9.2$, so:
$y = 1.2x + 9.2$

Step3: Match to the option

Combine the two equations into a system.

Answer:

$\boldsymbol{

$$\begin{cases} y = 0.8x + 12.4 \\ y = 1.2x + 9.2 \end{cases}$$

}$ (the first option)