Math Problem Statement
Which system is the solution of the graph?
alg2syin_QuizQu12.png
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
Solution
From the graph you provided, we see two linear inequalities:
- The line with a negative slope appears to be , and the shading is to the left (below) of this line, suggesting that the inequality is .
- The line with a positive slope appears to be , and the shading is above this line, suggesting that the inequality is .
This system corresponds to the third option:
\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.Ask a new question for Free
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Math Problem Analysis
Mathematical Concepts
Linear Inequalities
Graphing Systems of Inequalities
Formulas
y = -x + 2
y = x - 2
Theorems
Intersection of Linear Inequalities
Suitable Grade Level
Grades 8-10
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