Question

directions: use your knowledge of systems of linear equations and functions to answer the questions below. 4 pts each / 4 explain your answer if needed. 1 answer the questions below 2. which expression can you substitute for x in 5x + y = 8 to solve the system below? \\(\

$$\begin{cases}5x + y = 8 \\\\ x + 4y = 2\\end{cases}$$

\\) a 2 - 4y b -2 - 4y c 2 + 4y 2. answer the questions below. fill in the blanks to solve each system by substitution. the first one is started for you. use this system for 3–4. \\(\

$$\begin{cases}5x + y = 8 \\\\ x + 4y = 2\\end{cases}$$

\\) 3. select yes or no to tell if you can make the indicated substitution in 5x + y = 8 to solve the system. a 2 - 4y for x \\(\circ\\) yes \\(\circ\\) no b 8 + 5x for y \\(\circ\\) yes \\(\circ\\) no

Explanation:

Question 2

Step1: Solve the second equation for x

We have the equation \( x + 4y = 2 \). To solve for \( x \), we subtract \( 4y \) from both sides of the equation.
\( x + 4y - 4y = 2 - 4y \)
Simplifying the left side (since \( 4y - 4y = 0 \)), we get \( x = 2 - 4y \).

Step2: Determine the substitutable expression

So the expression we can substitute for \( x \) in \( 5x + y = 8 \) is \( 2 - 4y \), which corresponds to option A.

From Question 2, we found that \( x = 2 - 4y \) by solving \( x + 4y = 2 \) for \( x \). So substituting \( 2 - 4y \) for \( x \) in \( 5x + y = 8 \) is valid as it comes from the other equation in the system.

We start with the equation \( 5x + y = 8 \). If we try to solve for \( y \), we subtract \( 5x \) from both sides: \( y = 8 - 5x \), not \( 8 + 5x \). So substituting \( 8 + 5x \) for \( y \) is incorrect.

Answer:

A. \( 2 - 4y \)

Question 3

Part A