This key facts covers What Can We Solve Graphically? within Graphical Solutions for GCSE Mathematics. Revise Graphical Solutions in Algebra for GCSE Mathematics with 9 exam-style questions and 6 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 2 of 10 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
What Can We Solve Graphically?
| Equation Type | Graph Intersection | Solution Method |
|---|---|---|
| Linear Equation 2x - 3 = 0 |
Line crosses x-axis | Find x-intercept |
| Simultaneous Linear y = 2x + 1 y = -x + 4 |
Two lines intersect | Find crossing point coordinates |
| Quadratic Equation x² - 3x - 4 = 0 |
Parabola crosses x-axis | Find x-intercepts (roots) |
| Inequalities y ≥ 2x + 1 |
Region above/below line | Identify solution region |
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 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.
Quick recall flashcards
Intersection Point
The point where two graphs cross - this gives x and y values that satisfy both equations
Graphical Solution
Finding where two graphs intersect gives the solution to simultaneous equations