Question

1. steve gets 4 points for every correct answer and looses 1 point for every wrong answer. if he answered 30 questions and scored 20 points, write a system of equations.\\

\\(\

$$\begin{cases} r + w = 30 \\\\ 4r - 1w = 20 \\end{cases}$$

\\)\\
\\(\

$$\begin{cases} r + w = 30 \\\\ 4r + 1w = 20 \\end{cases}$$

\\)\\
\\(\

$$\begin{cases} r + w = 20 \\\\ 4r - 1w = 30 \\end{cases}$$

\\)\\
\\(\

$$\begin{cases} r + w = 20 \\\\ 4r + 1w = 30 \\end{cases}$$

\\)

Explanation:

Step1: Define variables

Let $r$ = number of correct answers, $w$ = number of wrong answers.

Step2: Total questions equation

Total answered questions: $r + w = 30$

Step3: Total score equation

Points from correct answers: $4r$, points lost from wrong answers: $1w$. Total score: $4r - w = 20$

Answer:

$\boldsymbol{

$$\begin{cases} r + w = 30 \\ 4r - 1w = 20 \end{cases}$$

}$ (matches the first option)