Math Problem Statement
Which point is a solution to the simultaneous inequality y < 1/2 xand y > 1/3 x + 3? A. (10, 5) B. (3, 6) C. (2, 2) D. (25, 12)
Solution
To determine which point is a solution to the simultaneous inequalities:
we'll substitute each point into these inequalities and see if both conditions are satisfied.
Checking Points
Option A: (10, 5)
- (False, since is not less than )
- (False, since is not greater than )
Conclusion: Not a solution.
Option B: (3, 6)
- (False, since is not less than )
- (True)
Conclusion: Not a solution.
Option C: (2, 2)
- (False, since is not less than )
- (False)
Conclusion: Not a solution.
Option D: (25, 12)
- (True)
- (True)
Conclusion: This point satisfies both inequalities.
Answer
The point that satisfies both inequalities is D. (25, 12).
Would you like further clarification or additional details?
Here are 5 related questions for deeper understanding:
- How do you graph linear inequalities on a coordinate plane?
- What is the process for finding the solution region for two inequalities?
- How can you check if a point lies in a shaded region on a graph?
- What does the boundary line of an inequality represent in a graph?
- How can simultaneous inequalities be used in real-world applications?
Tip: When checking inequalities, always evaluate each inequality independently to ensure each condition is satisfied.
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Inequalities
Coordinate Geometry
Formulas
y < (1/2)x
y > (1/3)x + 3
Theorems
Linear Inequality Theorem
Suitable Grade Level
Grades 9-10
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