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Sim. equ. graphically

Free Printable Sim. equ. graphically PDF Worksheets, Revision Guide & GCSE Past Paper Questions (Grade 5)

Download free sim. equ. graphically worksheets (PDF), GCSE maths past paper questions and worked solutions for Sim. equ. graphically (5N). This is a Grade 5 algebra topic from the GCSE questions by topic collection for Foundation and Higher tier crossover GCSE Maths (Edexcel, AQA, OCR and IGCSE).

The free PDF worksheets table below brings together printable question booklets (Qs) and worked answers or mark schemes (Ans) from Maths Genie, Corbett Maths, Maths Made Easy, Naiker Maths, Dr Austin, Metatutor, GCSE Maths Rocket, E Classroom and PMT, along with past paper question booklets.

Below the worksheet links you can read our sim. equ. graphically revision notes and worked examples with diagrams, try real GCSE past paper sim. equ. graphically questions with step-by-step solutions, or download a PDF of all sim. equ. graphically worksheet links.

Free Sim. equ. graphically PDF Worksheets & Answers

Grade 5 • Topic 5N
Resource Questions Answers
GCSE past paper questions & solutions
 Qs Ans
Graded exam questions & solutions
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Textbook Exercise & answers
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MME worksheet & model answers
 Qs Ans
Exam question booklet & solutions
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Practice grid / worksheet & answers
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Topic worksheet & worked solutions
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Practice questions & answers
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GCSE topic booklet & answers
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PMT (Edxl)
Edexcel GCSE topic questions & solutions
 Qs Ans
PMT (AQA)
AQA GCSE topic questions & solutions
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PMT (IGCSE)
Edexcel IGCSE topic questions & solutions
 Qs Ans
Interactive online lesson & practice
 Page
Grade 5 topics
5A - Combining ratios5B - Direct and inverse proportion
5C - Reverse percentages5D - Standard form
5E - Speed5F - Changing the subject
5G - Quadratic expressions5H - Solving quadratic equations
5J - Drawing quadratic graphs5K - Cubic/reciprocal graphs
5L - Simultaneous equations5M - Sector areas and arc lengths
5N - Sim. equ. graphically5P - Midpoint of a line segment
5Q - Gradient of a line5R - Equation of a line
5S - Spheres and cones5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)5V - Exact trig. values
5W - Probability trees5X - Vectors
5Y - Venn diagrams5Z - Density
5AA - Pressure
GCSE Maths Grade 5 Revision Notes & Method

Guide to Sim. equ. graphically: Explanation, Diagrams & Worked Examples

Download Printable One Page Guide (PDF)

Explanation:

To solve simultaneous equations graphically, plot both equations on the same set of axes and find the coordinates (x, y) of the point(s) where the graphs intersect. At an intersection point, both equations share the exact same x-value and y-value.

Two non-parallel straight lines cross at one point (one pair of solutions). A straight line and a quadratic curve can cross twice (two pairs of solutions), touch once as a tangent, or never meet (no real solutions).

Example 1: The lines y = 2x − 1 and x + y = 8 are drawn on a grid and cross at (3, 5). Write down the solution to the simultaneous equations.

Solution:

Read intersection coordinates:
x = 3, y = 5
Check: 2(3)−1 = 5; 3+5 = 8 ✓
Answer: x = 3, y = 5
(3, 5) y=2x−1 x+y=8

Example 2: The curve y = x2 − 3 and the line y = x + 3 intersect at (−2, 1) and (3, 6). Solve the simultaneous equations graphically.

Solution:

Read both intersections:
• (−2, 1) → x = −2, y = 1
• (3, 6) → x = 3, y = 6
Ans: (−2, 1) or (3, 6)
(−2,1) (3,6)
Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Sim. equ. graphically Questions & Answers

Past Paper Example 1 GCSE May 2023 1F Q28 / 1H Q9 1 mark
Full Paper (PDF) • Mark Scheme (PDF)
xy–551015–15–10–55O2y = 3x – 222 – 2y = x
Use the graphs to solve the simultaneous equations 2 – 2y = x and 2y = 3x – 22.
Use these graphs to solve the simultaneous equations
2 - 2y = x
2y = 3x - 22
Worked Solution & Mark Scheme (1 mark)
The lines intersect at (6, –2) B1
Answer: x = 6, y = –2
Past Paper Example 2 OCR Nov 2019 6H Q7 5 marks
Full Paper (PDF) • Mark Scheme (PDF)
(c) On the same grid, draw the graph of y = 2x - 6 for -1 ≤ x ≤ 5.
(d) Use your graphs to solve the equation x2 - 4x + 1 = 2x - 6.
Give your answers to 1 decimal place.
(c) On the same grid, draw the graph of y = 2x - 6 for -1 ≤ x ≤ 5. [3 marks]
(d) Use your graphs to solve the equation x2 - 4x + 1 = 2x - 6.
Give your answers to 1 decimal place. [2 marks]
Worked Solution & Mark Scheme (5 marks)
Part (c) Solution:
Plot (−1, −8), (0, −6), (3, 0), (5, 4) on the grid and join with a ruled straight line. M2 A1
Answer (c): Straight line drawn from (−1, −8) through (3, 0) to (5, 4)
Part (d) Solution:
Read the x-coordinates of the points of intersection of y = x² − 4x + 1 and y = 2x − 6: M1
x = 1.6 and x = 4.4 (or 1.5–1.7 and 4.3–4.5). A1
Answer (d): x = 1.6 or x = 4.4
Past Paper Example 3 OCR Jun 2025 5H Q7 6 marks
Full Paper (PDF) • Mark Scheme (PDF)
The graph of the line x + y = 3 is shown on this grid.
–5–4–3–2–1123456–4–3–2–112345yx0
(a) By drawing a suitable line on the grid, solve these simultaneous equations.
x + y = 3 and y = 2x - 3 [4 marks]
(b) Umi says,
The simultaneous equations y = 2x + 3 and 2y - 4x = 7 will have no solutions.
Is Umi correct?
Explain how you decide. [2 marks]
Worked Solution & Mark Scheme (6 marks)
Part (a) Solution:
Draw the ruled line y = 2x − 3 passing through (0, −3), (2, 1), (4, 5) M3
Point of intersection with x + y = 3 is (2, 1) ⇒ x = 2, y = 1. A1
Answer (a): x = 2, y = 1
Part (b) Solution:
2y − 4x = 7 ⇒ y = 2x + 3.5. M1
Both lines have the same gradient (2) and different y-intercepts, so they are parallel and never intersect. C1
Answer (b): Umi is correct because 2y − 4x = 7 rearranges to y = 2x + 3.5, so both lines have gradient 2 and are parallel.

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