Mathematics
Grade 11
15 min
Is (x, y) a solution to the system of inequalities?
Is (x, y) a solution to the system of inequalities?
What you'll learn
- Identify the value of different coins and bills (pennies, nickels, dimes, quarters, one-dollar bills, five-dollar bills) with 100% accuracy.
- Solve word problems involving adding money amounts up to $10.00 with at least 80% accuracy, showing your work.
- Solve word problems involving subtracting money amounts up to $10.00 with at least 80% accuracy, showing your work.
- Explain how to add or subtract money amounts using strategies like counting up or drawing pictures with at least 75% accuracy.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Substitute an ordered pair (x, y) into a system of linear and non-linear inequalities.
Evaluate each inequality in a system to determine if it results in a true or false statement.
Define what constitutes a solution to a system of inequalities.
Apply the 'Simultaneous Truth Condition' to determine if an ordered pair is a solution to the entire system.
Differentiate between strict (<, >) and non-strict (≤, ≥) inequalities when verifying solutions.
Explain why a point that satisfies only one inequality in a system is not a solution to the system.
Can a single location be both north of the river AND west of the mountains? 🗺️ Just like a point on a map, a mathematical point must satisfy ALL conditions to be in the solution region.
This tutori...
2
Key Concepts & Vocabulary
TermDefinitionExample
System of InequalitiesA set of two or more inequalities containing the same variables. The solution to the system is the set of all ordered pairs that make all inequalities in the set true.y > 2x - 1 and y ≤ -x + 5
Ordered PairA pair of numbers, written as (x, y), that represents a point's location on a Cartesian plane.(3, 4) represents a point where x=3 and y=4.
Solution to a System of InequalitiesAn ordered pair (x, y) that, when substituted into every inequality in the system, makes every inequality a true statement.For the system y > x and y < 5, the point (2, 3) is a solution because 3 > 2 is true and 3 < 5 is true.
Strict InequalityAn inequality that uses the symbols > (greater than) or < (less than). The boundary line or curve is not...
3
Core Formulas
The Substitution and Verification Principle
For a given point (x_0, y_0) and an inequality in two variables, substitute x_0 for x and y_0 for y. Then, simplify to determine if the resulting statement is true or false.
This is the fundamental process used to test a single point against a single inequality. It's the first step in checking a solution for a system.
The Simultaneous Truth Condition
An ordered pair (x_0, y_0) is a solution to a system of inequalities if and only if it satisfies EVERY inequality in the system. If (x_0, y_0) makes even one inequality false, it is NOT a solution to the system.
Use this as the final decision-making rule. After testing the point in all inequalities, if you have all 'true' results, it's a solution. If you have one or...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Is the point (2, 1) a solution to the system involving an ellipse: { x²/9 + y²/4 ≤ 1, y > x - 2 }?
A.No, because it fails the ellipse inequality.
B.Yes, because it satisfies both inequalities.
C.No, because it fails the linear inequality.
D.Yes, because satisfying the ellipse inequality is sufficient.
Challenging
Is the point (2, 5) a solution to the complex system: { y ≥ x² + 1, y < -x + 4, x² + y² < 30 }?
A.Yes, it satisfies all three inequalities.
B.No, it fails only the first inequality.
C.No, it fails only the third inequality.
D.No, it fails only the second inequality.
Challenging
Given that (2, k) is a solution to the system { y < x² - 1, y > -x + 3 }, what is a possible integer value for k?
A.1
B.3
C.2
D.0
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Systems of inequalities
Mathematics for other grades
Frequently asked questions
What grade level is "Is (x, y) a solution to the system of inequalities?"?
Is (x, y) a solution to the system of inequalities? is a Grade 11 Mathematics lesson on ExcelOS.
What will I learn in Is (x, y) a solution to the system of inequalities??
You'll be able to: Identify the value of different coins and bills (pennies, nickels, dimes, quarters, one-dollar bills, five-dollar bills) with 100% accuracy; Solve word problems involving adding money amounts up to $10.00 with at least 80%….
Is "Is (x, y) a solution to the system of inequalities?" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Is (x, y) a solution to the system of inequalities??
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.