Graphical Solution of Simultaneous Linear Inequalities

Understanding Linear Inequalities

Linear inequalities are similar to linear equations, but instead of an equal sign, they use inequality symbols such as <, >, ≤, and ≥. Solving them graphically involves finding the region that satisfies all the inequalities in a system.

For example, consider the inequalities:

• $x + y \leq 4$

• $x - y \geq 1$

Steps to Solve Graphically

1. Graph Each Inequality: Convert each inequality to an equation by replacing the inequality sign with an equal sign. Graph these lines on a coordinate plane.
2. Determine the Shaded Region: For each inequality, determine which side of the line to shade. This is usually done by testing a point not on the line (often the origin, $(0,0)$, if it is not on the line).
3. Find the Intersection: The solution to the system of inequalities is the region where the shaded areas overlap.

Worked Example

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