# Linear inequalities in two variables

The solution of a linear inequality in two variables like Ax + By > C is an ordered pair (x, y) that produces a true statement when the values of x and y are substituted into the inequality.

Example:

Is (1, 2) a solution to the inequality

$\\ 2x+3y>1 \\\\2\cdot 1+3\cdot 2\overset{?}{>}1 \\2+5\overset{?}{>}1 \\7>1 \\$

The graph of an inequality in two variables is the set of points that represents all solutions to the inequality. A linear inequality divides the coordinate plane into two halves by a boundary line where one half represents the solutions of the inequality. The boundary line is dashed for > and < and solid for ≤ and ≥. The half-plane that is a solution to the inequality is usually shaded.

Example:

Graph the inequality

$\\ y\geq -x+1 \\$

Videolesson: Graph the linear inequality

$\\y \geq 2x -3\\$

Next Class:  Systems of linear equations and inequalities, Graphing linear systems
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