EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: Solving simultaneous equations graphically
Solving simultaneous equations graphically · Equations and graphs · Lesson 1 of 6 · 17 marks · 25 minutes
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Instructions
• Answer all the questions.
• Write your answers in the spaces provided.
• The marks for each question are shown in brackets - use this as a guide to how much to write.
• The answers are on separate pages at the back. Attempt every question before you look at them.
• Answer all questions. Show your working.
Question 1 DRAW (4 marks)
The graph of y = 2x − 1 is drawn on the grid. On the grid, draw the graph of x + y = 5. Hence solve the simultaneous equations y = 2x − 1 and x + y = 5.
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(Total for Question 1 = 4 marks)
Question 2 SOLVE (3 marks)
Use a graph to solve y = x − 1 and y = 5 − x, for values of x from 0 to 5.
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(Total for Question 2 = 3 marks)
Question 3 SHOW THAT (3 marks)
The lines y = 3x − 2 and y = x + 4 cross at the point (3, 7). Show that x = 3 and y = 7 satisfy both equations.
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(Total for Question 3 = 3 marks)
Question 4 EXPLAIN (2 marks)
Explain why the simultaneous equations y = 2x + 1 and y = 2x + 5 have no solutions.
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(Total for Question 4 = 2 marks)
Question 5 SOLVE (3 marks)
The lines y = 2x + 1 and y = 7 − x are drawn on a grid. They meet at a single point. Find the coordinates of the point using algebra, and say how you could check this on the graph.
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(Total for Question 5 = 3 marks)
Question 6 WRITE DOWN (2 marks)
The graph shows two lines crossing at (4, −1). Write down the solution to the pair of simultaneous equations.
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(Total for Question 6 = 2 marks)
TOTAL FOR PAPER = 17 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (4 marks)
The line x + y = 5 passes through (0, 5), (2, 3) and (5, 0). The lines cross at (2, 3), so x = 2 and y = 3.
• Two correct points for the second line M1
• Correct line drawn A1
• Intersection identified M1
• x = 2, y = 3 A1
Question 2 (3 marks)
The lines cross at (3, 2), so x = 3 and y = 2.
• Table or points for both lines M1
• Both lines drawn A1
• x = 3, y = 2 A1
Question 3 (3 marks)
3 × 3 − 2 = 7, and 3 + 4 = 7. Both are true.
• Substitutes into first M1
• Substitutes into second M1
• Both correct A1
Question 4 (2 marks)
Both lines have gradient 2, so they are parallel and never meet.
• Same gradient M1
• Parallel, so no intersection C1
Question 5 (3 marks)
2x + 1 = 7 − x, so 3x = 6, x = 2, y = 5. The point is (2, 5). On the graph both lines pass through (2, 5).
• Equates the two y values M1
• x = 2 A1
• y = 5 A1
Question 6 (2 marks)
x = 4 and y = −1
• x = 4 B1
• y = −1 B1