Math Problem Statement
A system of inequalities is shown below:
y<−2x+1y<−2x+1
x+2y≥−4x+2y≥−4
Which of the following is in the solution set of this system of inequalities?
A.(−9,1)(−9,1)
B.(−5,4)(−5,4)
C.(2,−3)(2,−3)
D.(6,−8)(6,−8)
Solution
To determine which point is in the solution set of this system of inequalities, we need to test each given point against the two inequalities:
Test Point A:
- For :
- For : Thus, point A does not satisfy both inequalities.
Test Point B:
- For :
- For : Thus, point B satisfies both inequalities.
Test Point C:
- For : Thus, point C does not satisfy the first inequality.
Test Point D:
- For : Thus, point D does not satisfy the first inequality.
Conclusion:
The only point that satisfies both inequalities is B: .
Do you need further explanation or any additional details? Here are five related questions to expand your understanding:
- How do you graph systems of inequalities on a coordinate plane?
- How would the solution set look visually for this system?
- How can you determine if a system of inequalities has no solution?
- What happens if both inequalities have the same slope?
- Can inequalities with different variables (like and ) be solved similarly?
Tip: When testing a point in an inequality, plug the coordinates into both inequalities and check for consistency with the inequality signs.
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Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Systems of Inequalities
Formulas
y < −2x + 1
x + 2y ≥ −4
Theorems
Testing Points in Inequalities
Intersection of Solution Sets
Suitable Grade Level
Grades 8-10
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