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Method 4: Solving Inequalities Graphically

Part of Graphical Solutions — GCSE Mathematics

This deep dive covers Method 4: Solving Inequalities Graphically within Graphical Solutions for GCSE Mathematics. Revise Graphical Solutions in Algebra for GCSE Mathematics with 9 exam-style questions and 6 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 7 of 9 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 7 of 9

Practice

9 questions

Recall

6 flashcards

Method 4: Solving Inequalities Graphically

  1. Plot boundary line (solid if ≤/≥, dashed if
  2. Choose test point not on the line (often use origin if convenient)
  3. Substitute coordinates into inequality
  4. Shade correct region: if test point satisfies inequality, shade that side
  5. Check solution by testing another point in shaded region

Keep building this topic

Read this section alongside the surrounding pages in Graphical Solutions. That gives you the full topic sequence instead of a single isolated revision point.

Worked Example 2: Simultaneous Linear EquationsWorked Example 4: Linear InequalityWhere Algebra Meets GraphsWhat Can We Solve Graphically?

Practice Questions for Graphical Solutions

A straight line y = 3x − 6 is plotted on a graph. Where does the solution to 3x − 6 = 0 appear on the graph?

  • A. Where the line crosses the y-axis
  • B. Where the line crosses the x-axis
  • C. At the origin
  • D. At the turning point of the line
1 markfoundation

A student tries to solve the simultaneous equations y = 3x + 2 and y = 3x − 5 graphically. Explain what they will see on the graph and what this means for the solution.

2 marksstandard

Quick Recall Flashcards

Graphical Solution
Finding where two graphs intersect gives the solution to simultaneous equations
Intersection Point
The point where two graphs cross - this gives x and y values that satisfy both equations

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Worked Example 2: Simultaneous Linear Equations

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Worked Example 4: Linear Inequality