Systems of Inequalities in Two Variables

A system of inequalities in two variables consists of two or more inequalities with the same two variables, typically x and y. These systems can have zero solutions, one solution, multiple (but finite) solutions, or an infinite number of solutions. It is often helpful to graph system of inequalities in two variables, as the solutions of the system will be the points/lines/regions where all inequalities in the system overlap.

Examples:

• $x>4$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y < -4 }
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y \geq x + 1 } , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y \leq < x^2 } , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y < 4 }
• Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x + y < 1 } , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 + y^2 < 1 }

Resources

• Systems of Linear Inequalities in Two Variables, Lumen Learning
• Solving Systems of Inequalities, Textbook Tactics on YouTube
• Graphing Systems of Linear Inequalities with Two Variables, Math Planet