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.
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 ✓
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 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.