Math Problem Statement
Is (1, 10) a solution to this system of inequalities?
y ≥ 8x + 2 y ≥ x + 10
Solution
To determine if is a solution to the system of inequalities, we need to substitute and into each inequality and check if they hold true.
Step 1: Substitute into each inequality
-
First inequality:
- Substitute and :
- Simplify the right side: This inequality holds because .
-
Second inequality:
- Substitute and :
- Simplify the right side: This inequality does not hold because .
Conclusion
Since the point does not satisfy the second inequality, it is not a solution to the system of inequalities.
Would you like further explanation on solving systems of inequalities?
- How can I determine if a point lies in the solution set of multiple inequalities?
- What strategies can I use to graph inequalities on a coordinate plane?
- How do I check solutions for inequalities with strict inequalities (e.g., or )?
- Can a point be a solution for one inequality but not the entire system?
- What is the difference between systems of inequalities and systems of equations?
Tip: Always test each inequality separately when working with systems of inequalities.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Algebra
Inequalities
Systems of Inequalities
Formulas
y ≥ 8x + 2
y ≥ x + 10
Theorems
Substitution Method for Inequalities
Suitable Grade Level
Grades 9-11
Related Recommendation
Is (3, 10) a Solution to the System of Inequalities y < x + 8 and y < 7x + 5?
Is (8, 4) a Solution to the System of Inequalities y > x + 8, x ≥ 8?
Determine if (2,10) is a Solution to the System of Inequalities y > 3x + 3, y > x + 10
Determine Points Not Satisfying a System of Linear Inequalities
Solution to the System of Inequalities y < 10 and 9x - 8y < -10