Sheet № 199 · Foundation + Higher · AQA · Edexcel · OCR
Simultaneous Equations Graphically –
Solving simultaneous equations graphically is a visual approach that appears on both Foundation and Higher GCSE Maths papers. Instead of using algebra, you plot both equations on the same axes and read the solution from where the lines cross.
§Key definitions
Question:
Solve the simultaneous equations y = 2x + 1 and y = -x + 7 graphically.
Answer:
x = 2, y = 5
Q1 (Foundation):
Solve graphically: y = x + 3 and y = -x + 5.
Q2 (Foundation):
Solve graphically: y = 3x - 1 and y = x + 5.
Q3 (Higher):
The line y = 2x + 1 and the curve y = x² intersect at two points. Find their coordinates.
§Formulas to memorise
The solution is the coordinates (x, y) of the point of intersection
Rearrange each equation into the form y = mx + c if it is not already.
Worked example
Solve the simultaneous equations y = 2x + 1 and y = -x + 7 graphically.
Working:
⚠ Common mistakes
- ✗Inaccurate plotting or reading. Even a small error in plotting can shift the intersection point. Use a sharp pencil and plot points carefully.
- ✗Forgetting to check the answer. Always substitute back into both equations. If the values do not satisfy both, re-read the graph.
- ✗Not drawing lines far enough. If your lines do not extend to where they intersect, you cannot read the solution. Choose x values that cover a wide enough range.
✦ Exam tips
- →Use a ruler for straight-line graphs — freehand lines lose accuracy and marks.
- →If the intersection falls between gridlines, give your answer to the nearest half or state "approximately."
- →If the question provides a pre-drawn graph, you only need to read the intersection — do not re-plot.