GraphsDeep Dive

Solving Simultaneous Equations Graphically

Part of Linear Graphs Problems · GCSE GCSE Mathematics revision

This deep dive covers Solving Simultaneous Equations Graphically within Linear Graphs Problems for GCSE Mathematics. Revise Linear Graphs Problems in Graphs for GCSE Mathematics with 16 exam-style questions and 11 flashcards. Use this page as part of a wider topic revision path rather than treating it as an isolated fact. It is section 4 of 10 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 4 of 10

Practice

16 questions

Recall

11 flashcards

Solving Simultaneous Equations Graphically

When two straight-line equations share a solution (x, y), the lines cross at that point. The crossing point is the solution to both equations simultaneously.

Draw both lines on the same axes (plot at least 3 points each)
Find where the lines intersect
Read the x and y coordinates of the intersection point
State the solution: x = ?, y = ?

No solution: If lines are parallel (same gradient, different intercepts), they never cross — the simultaneous equations have no solution.

Infinite solutions: If both equations give the same line, every point is a solution.

Example: Solve y = 2x + 1 and y = −x + 7 graphically.

Draw both lines. They cross at x = 2, y = 5.

Solution: x = 2, y = 5.

Check: 2(2) + 1 = 5 ✓ and −2 + 7 = 5 ✓

Keep building this topic

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

Finding the Equation of a Line Real-Life Linear Graphs — Interpreting Context Lines in the Real World The Equation y = mx + c — Quick Reference

Practice Questions for Linear Graphs Problems

A taxi company charges a fixed fee plus an amount per mile. On a cost graph (£ against miles), what does the y-intercept represent?

A. The cost per mile
B. The total cost of the journey
C. The fixed charge before any miles are travelled
D. The gradient of the line

1 markfoundation

A plumber charges according to the formula C = 40t + 30, where C is the total cost in pounds and t is the time in hours. Explain what the values 40 and 30 represent in this context.

2 marksstandard

Quick Recall Flashcards

Steps to find the equation of a line from a graph

1. Read the y-intercept (c) where line crosses y-axis 2. Choose two clear points on the line 3. Calculate gradient m = (y2 - y1)/(x2 - x1) 4. Write y = mx + c Example: crosses (0, 1), gradient 2 → y = 2x + 1

What does each letter in y = mx + c represent?

y = mx + c m = gradient (steepness of the line) c = y-intercept (where the line crosses the y-axis) Example: y = 3x + 2 has gradient 3 and crosses y-axis at (0, 2).

16 questions on Linear Graphs Problems — practise free

Instant marking, adaptive difficulty, and 11 spaced repetition flashcards. Free until your GCSEs.

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Finding the Equation of a Line

Real-Life Linear Graphs — Interpreting Context