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

$$y\geq -x+1$$

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Video lesson

Graph the linear inequality

$$y \geq 2x -3$$