Question

use the graph to determine the number of solutions the system has. then state whether the system of equations is consistent or inconsistent and if it is independent or dependent.
$2x + 2y = 8$
$y = -x + 4$

Explanation:

Step1: Simplify first equation

$$\begin{align} 2x + 2y &= 8 \\ \frac{2x + 2y}{2} &= \frac{8}{2} \\ x + y &= 4 \\ y &= -x + 4 \end{align}$$

Step2: Compare the two equations

The simplified first equation $y = -x + 4$ is identical to the second given equation $y = -x + 4$. On the graph, this means they are the same line, overlapping completely.

Step3: Classify the system

A system where equations represent the same line has infinitely many solutions. Systems with at least one solution are consistent, and identical equations form a dependent system.

Answer:

The system has infinitely many solutions. The system is consistent and dependent.