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Which system is the solution of the graph?

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Group of answer choices

open curly brackets table attributes columnalign left end attributes row cell y space greater or equal than space x space plus space 2 end cell row cell y space greater or equal than space x space minus space 2 end cell end table close

open curly brackets table attributes columnalign left end attributes row cell y space less than thin space minus x space plus space 2 end cell row cell y space greater than space x space minus space 2 end cell end table close

open curly brackets table attributes columnalign left end attributes row cell y space less or equal than space minus x space plus space 2 end cell row cell y space greater or equal than space x space minus space 2 end cell end table close

open curly brackets table attributes columnalign left end attributes row cell y space greater or equal than space minus x space plus space 2 end cell row cell y space less or equal than space x space minus space 2 end cell end table close

From the graph you provided, we see two linear inequalities:

1. The line with a negative slope appears to be \( y = -x + 2 \), and the shading is to the left (below) of this line, suggesting that the inequality is \( y \leq -x + 2 \).
2. The line with a positive slope appears to be \( y = x - 2 \), and the shading is above this line, suggesting that the inequality is \( y \geq x - 2 \).

This system corresponds to the third option:

\[
\left\{
\begin{aligned}
y & \leq -x + 2 \\
y & \geq x - 2
\end{aligned}
\right.
\]

Would you like more details or have any questions?

Here are 5 related questions to consider:

1. How do you graph a linear inequality like \( y \geq x - 2 \)?
2. What is the significance of the shaded region in a system of inequalities?
3. How can you check if a point is a solution to a system of inequalities?
4. What changes if the inequalities are strict (e.g., \( y < x - 2 \)) instead of inclusive (e.g., \( y \leq x - 2 \))?
5. How does the solution of a system of inequalities relate to the intersection of regions?

**Tip:** Always test a point from the shaded region to verify that it satisfies the system of inequalities.

Which system is the solution of the graph?

This guide explains how to find the solution to the system of linear inequalities y ≤ -x + 2 and y ≥ x - 2 by analyzing the graph. Learn key concepts such as graphing inequalities, determining shading regions, and identifying intersection points. Suitable for students in Grades 8-10.

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