Solving Linear Systems & Inequalities

A solution to a linear inequality is any point (x, y) that makes the inequality true, typically represented in a shaded region on a graph.

A dotted line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict, such as < or >).

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict, such as ≤ or ≥).

A point is a solution to a system of inequalities if it lies in the shaded region of all inequalities in the system.

The graphical representation is two lines that overlap completely, meaning every point on the line is a solution.

The first step is to solve one of the equations for one variable in terms of the other variable.

The solution is (1, 5).

It means that the lines representing the equations are parallel and never intersect.

A linear equation represents a straight line, while a linear inequality represents a region of the graph that satisfies the inequality.

You can substitute the point's coordinates into the inequality to see if it makes the inequality true.