EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Exam Practice: More Simultaneous Equations
More simultaneous equations · Equations and inequalities · Lesson 6 of 7 · 23 marks · 35 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 NON-CALCULATOR (4 marks)
Solve the simultaneous equations 2x + 3y = 13 and 5x − 2y = 4.
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(Total for Question 1 = 4 marks)
Question 2 NON-CALCULATOR (4 marks)
Solve the simultaneous equations 3x + 2y = 12 and 5x − 3y = 1.
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(Total for Question 2 = 4 marks)
Question 3 NON-CALCULATOR (4 marks)
The sum of two numbers is 25. Twice the first number plus three times the second number is 62. Work out the two numbers.
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(Total for Question 3 = 4 marks)
Question 4 CALCULATOR (4 marks)
3 apples and 2 bananas cost £1.80. 2 apples and 5 bananas cost £2.30. Work out the cost of one apple and the cost of one banana.
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(Total for Question 4 = 4 marks)
Question 5 NON-CALCULATOR (3 marks)
Find the coordinates of the point where the lines y = 3x − 2 and y = x + 4 cross.
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(Total for Question 5 = 3 marks)
Question 6 NON-CALCULATOR (4 marks)
Solve the simultaneous equations 4x + y = 14 and 2x − 3y = 0.
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(Total for Question 6 = 4 marks)
TOTAL FOR PAPER = 23 MARKS
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Answers and mark scheme
Check your answer only once you have written one.
Question 1 (4 marks)
Multiplying gives 4x + 6y = 26 and 15x − 6y = 12. Adding gives 19x = 38, so x = 2. Then 4 + 3y = 13, so y = 3.
• Multiplying to match coefficients M1
• 19x = 38 M1
• x = 2 A1
• y = 3 A1
Question 2 (4 marks)
Multiplying gives 9x + 6y = 36 and 10x − 6y = 2. Adding gives 19x = 38, so x = 2 and y = 3.
• Multiplying to match coefficients M1
• 19x = 38 M1
• x = 2 A1
• y = 3 A1
Question 3 (4 marks)
x + y = 25 and 2x + 3y = 62. Subtracting twice the first from the second gives y = 12, so x = 13.
• Forming both equations M1
• A correct elimination step M1
• y = 12 A1
• x = 13 A1
Question 4 (4 marks)
3a + 2b = 180 and 2a + 5b = 230 (pence). Multiplying gives 6a + 4b = 360 and 6a + 15b = 690. Subtracting gives 11b = 330, b = 30, and a = 40. An apple costs 40p and a banana 30p.
• Forming both equations M1
• Multiplying to match M1
• b = 30 or a = 40 A1
• Both correct with units A1
Question 5 (3 marks)
3x − 2 = x + 4, so 2x = 6 and x = 3. Then y = 7. The point is (3, 7).
• Equating the two expressions M1
• x = 3 A1
• (3, 7) A1
Question 6 (4 marks)
From the second, x = 1.5y. Then 6y + y = 14, so y = 2 and x = 3. (Or multiply the first by 3 and add.)
• A method to eliminate or substitute M1
• 7y = 14 or 14x = 42 M1
• y = 2 A1
• x = 3 A1