Is (x, y) a solution to the system of inequalities?

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...

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...

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...