## Systems of Linear Inequalities in Two Variables

 6.2 Systems of Linear Inequalities in Two Variables
System of Linear Inequalities
 Definition
A combination of two or more linear inequalities.
 Determine The Appropriate Inequality for a Certain Situation
 Example of Situation Linear Inequality $$y$$ is greater than $$x$$ $$y>x$$ $$y$$ is less than $$x$$ $$y < x$$ $$y$$ is not less than $$x$$ $$y\geq x$$ $$y$$ is not more than $$x$$ $$y\leq x$$ $$y$$ is at least $$k$$ times $$x$$ $$y\geq kx$$ $$y$$ is at most $$k$$ times $$x$$ $$y\leq kx$$ Maximum of $$y$$ is $$k$$ $$y\leq k$$ Minimum of $$y$$ is $$k$$ $$y\geq k$$ Sum of $$x$$ and $$y$$ is greater than $$k$$ $$x+y >k$$ Difference between $$y$$ and $$x$$ is less than $$k$$ $$y-x Determine and Shade The Region That Satisfies a System of Linear Inequalities 1. Mark the region involved for each linear inequality with different and easily spotted markings. 2. Identify the common region for all the markings inolved. 3. Shade the common region completely. Make sure that the shading is not outside the common region.  Example Shade the region Problems Involving System of Linear Inequalities in Two Variables  Example ## Systems of Linear Inequalities in Two Variables  6.2 Systems of Linear Inequalities in Two Variables System of Linear Inequalities  Definition A combination of two or more linear inequalities.  Determine The Appropriate Inequality for a Certain Situation  Example of Situation Linear Inequality \(y$$ is greater than $$x$$ $$y>x$$ $$y$$ is less than $$x$$ $$y < x$$ $$y$$ is not less than $$x$$ $$y\geq x$$ $$y$$ is not more than $$x$$ $$y\leq x$$ $$y$$ is at least $$k$$ times $$x$$ $$y\geq kx$$ $$y$$ is at most $$k$$ times $$x$$ $$y\leq kx$$ Maximum of $$y$$ is $$k$$ $$y\leq k$$ Minimum of $$y$$ is $$k$$ $$y\geq k$$ Sum of $$x$$ and $$y$$ is greater than $$k$$ $$x+y >k$$ Difference between $$y$$ and $$x$$ is less than $$k$$ \(y-x

Determine and Shade The Region That Satisfies a System of Linear Inequalities
1. Mark the region involved for each linear inequality with different and easily spotted markings.
2. Identify the common region for all the markings inolved.
3. Shade the common region completely. Make sure that the shading is not outside the common region.
 Example