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

Learning Objectives Define a system of linear inequalities and its solution. Substitute the coordinates of an ordered pair (x, y) into a linear inequality. Evaluate whether a substituted inequality results in a true or false statement. Systematically test an ordered pair against all inequalities in a given system. Determine if an ordered pair is a solution to a system of inequalities based on the test results. Explain why an ordered pair is or is not a solution to a system. Ever tried to pick a movie that is under 2 hours long AND has a rating of over 80%? 🎬 You're already checking for solutions to a system of inequalities! In this tutorial, you will learn a straightforward method to check if a specific point (x, y) is a valid solution to a system of linear inequaliti...

TermDefinitionExample Linear InequalityA mathematical statement that compares two expressions using an inequality symbol (<, >, ≤, ≥), where at least one expression is linear. It describes a region on the coordinate plane.y < 2x + 3 System of Linear InequalitiesA set of two or more linear inequalities that are considered together. A solution must work for all of them simultaneously.{ y ≥ x - 4, y < -x + 5 } Ordered PairA pair of numbers, written as (x, y), that represents a specific point on a coordinate plane.(4, 1) Solution to an InequalityAn ordered pair (x, y) that makes the inequality a true statement when its values are substituted for the variables.For y > x, the point (3, 5) is a solution because substituting gives 5 > 3, which is true. Solution to a System of In...

The Substitution Principle For a given point (x_0, y_0) and an inequality like y < mx + b, substitute x_0 for x and y_0 for y to check if the statement y_0 < mx_0 + b is true. This is the fundamental action for testing a point. You replace the variables with the given numbers to see if the inequality holds true. The All-or-Nothing Rule A point (x_0, y_0) is a solution to a system {I_1, I_2, ..., I_n} if and only if (x_0, y_0) satisfies I_1 AND I_2 AND ... AND I_n. This is the master rule for systems. A point must satisfy every single inequality without exception. If even one test results in a false statement, the point is not a solution to the system.