5.11F Simultaneous Equations: Foundation Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 45 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Work out the value of x and y that satisfy both equations.

x = 3
2x + y = 8

(Total for Question 1 is 1 mark)

Solve the simultaneous equations by substitution.

y = 2x + 1
x + y = 10

(Total for Question 2 is 2 marks)

Use elimination to solve these equations.

2x + y = 11
x + 2y = 10

(Total for Question 3 is 2 marks)

Alf and Bea share some pens and pencils.

Alf buys 2 pens and 3 pencils for 9 pounds.
Bea buys 1 pen and 4 pencils for 7 pounds.

Let p be the price of a pen, in pounds, and q be the price of a pencil, in pounds. Write the simultaneous equations and solve for p and q.

(Total for Question 4 is 3 marks)

Solve the simultaneous equations. Give your answers as integers.

3x - y = 5
x + y = 7

(Total for Question 5 is 4 marks)

A small theatre has tickets for adults and children. An adult ticket costs 7 pounds and a child ticket costs 3 pounds.

On Monday the theatre sold 50 tickets and took 274 pounds.

Let a be the number of adult tickets and c the number of child tickets. Write the simultaneous equations and find a and c.

(Total for Question 6 is 5 marks)

Solve these simultaneous equations by elimination. Show your working clearly.

4x + 3y = 25
2x - y = 4

(Total for Question 7 is 6 marks)

A grocer mixes two sizes of fruit bags. A small bag contains 2 apples and 3 pears. A large bag contains 5 apples and 2 pears.

He makes some small bags and some large bags. In total there are 34 apples and 29 pears.

Let s be the number of small bags and L the number of large bags. Form the simultaneous equations and solve for s and L. Give your answers as integers.

(Total for Question 8 is 7 marks)

Mark scheme · 5.11F Simultaneous Equations: Foundation Tier Practice

Question 1

B1 x = 3, y = 2 cao
Answer: x = 3, y = 2

Question 2

M1 substitute y = 2x + 1 into x + y = 10 leading to x + 2x + 1 = 10 or 3x + 1 = 10
A1 x = 3 cao; then y = 7 cao
Answer: x = 3, y = 7

Question 3

M1 eliminate a variable, e.g. multiply first equation by 2 and subtract or subtract equations to get x or y
A1 x = 4, y = 3 cao
Answer: x = 4, y = 3

Question 4

M1 form equations: 2p + 3q = 9 and 1p + 4q = 7
M1 solve the two equations to find p and q, e.g. substitute or eliminate
A1 p = 3, q = 1 cao
Answer: p = 3, q = 1

Question 5

M1 add the two equations to eliminate y giving 4x = 12
A1 x = 3 cao
M1 substitute x = 3 into x + y = 7 to find y
A1 y = 4 cao
Answer: x = 3, y = 4

Question 6

M1 form equations: a + c = 50 and 7a + 3c = 274
M1 eliminate a or c, e.g. multiply first equation by 3 and subtract from second to get 4a = 274 - 150 = 124
A1 a = 31 cao
M1 substitute a = 31 into a + c = 50 to find c
A1 c = 19 cao
Answer: a = 31, c = 19

Question 7

M1 multiply second equation by 3 to align y: 6x - 3y = 12
M1 add to first equation to eliminate y giving 10x = 37
A1 x = 37/10 (or 3.7) cao
M1 substitute x = 37/10 into 2x - y = 4 to find y
A1 y = 17/5 cao
A1 final answers x = 37/10, y = 17/5 cao
Answer: x = 37/10, y = 17/5

Question 8

M1 form equations: 2s + 5L = 34 and 3s + 2L = 29
M1 eliminate a variable, e.g. multiply first equation by 3 and second by 2 to align s: 6s + 15L = 102 and 6s + 4L = 58
M1 subtract to get 11L = 44
A1 L = 4 cao
M1 substitute L = 4 into 2s + 5L = 34 to find s
A1 s = 7 cao
A1 final answers s = 7, L = 4 cao
Answer: s = 7, L = 4

Simultaneous Equations: Foundation Tier Practice - Worksheets, Questions and Revision