Does (x, y) satisfy the inequality?

Learning Objectives Define what it means for an ordered pair to be a solution to a linear inequality. Substitute the x and y values from an ordered pair into a given linear inequality. Evaluate the resulting numerical statement to determine if it is true or false. Confidently conclude whether a given ordered pair satisfies an inequality. Differentiate between strict inequalities (<, >) and non-strict inequalities (≤, ≥) when testing points. Explain that a solution to a linear inequality is any point within the shaded region of its graph. Planning a party and have a budget? Let's say you can spend *at most* $50 on pizza and soda. How do you check if buying 3 pizzas and 5 sodas works? 🤔 This tutorial will teach you a straightforward algebraic method to check if an...

TermDefinitionExample Linear InequalityA mathematical statement that compares two linear expressions using an inequality symbol (<, >, ≤, or ≥). It describes a region on the coordinate plane.y > 2x - 1 Ordered Pair (x, y)A pair of numbers, written in the form (x, y), that represents a specific location on a coordinate plane.(4, 5), where x=4 and y=5. SolutionAn ordered pair that makes the inequality a true statement when its values are substituted for x and y.For the inequality y < x, the point (3, 1) is a solution because 1 < 3 is a true statement. To SatisfyAn ordered pair 'satisfies' an inequality if it is a solution. This means it makes the inequality true.The point (5, 10) satisfies the inequality y ≥ 2x because substituting gives 10 ≥ 2(5), which simplifies...

The Substitution Method Given an inequality and a point (x₀, y₀), substitute x₀ for every 'x' and y₀ for every 'y' in the inequality. This is the first and most critical step. It transforms the algebraic inequality into a numerical statement that can be tested for truth. The Truth Test After substituting, simplify both sides of the inequality. If the resulting statement is mathematically true, the point is a solution. If it is false, the point is not a solution. This is the final check. A true statement like 5 > 2 means the point works. A false statement like 10 < 7 means the point does not.