Introduction to Simultaneous Equations - Worksheets, Questions and Revision

20 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 6)Introduction to Simultaneous Equations revision guide

This topic is chapter 4 of KS3 Maths: Algebra Practice Book 2.

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2.17 Introduction to Simultaneous Equations

AQA KS3.M-A17 · Calculators not allowed · about 60 minutes

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Solve the pair of equations using elimination.

(a)Eliminate x by subtracting the second equation from the first and find y, then x.(3)

Solve this pair by substitution where one equation is rearranged first.

(a)Rearrange 3x - y = 7 to express y in terms of x, substitute into x + 2y = 4 and solve.(3)

Solve by elimination after multiplying one equation.

(a)Multiply the first equation so you can eliminate x or y, then solve.(3)

Solve the pair where elimination needs different multipliers.

(a)Use elimination by making coefficients of x or y equal and solve both values.(4)

State whether x = 3, y = 4 satisfies the equation x + y = 7.

(1)

Solve the pair of equations by substitution.
y = x + 1 and x + y = 9. Find x and y.

(2)

Solve the pair of equations by substitution.
y = 2x - 1 and 3x + y = 14. Find x and y.

(2)

Solve the pair of equations by elimination.
x + y = 4 and x - y = 10. Find x and y.

(2)

Solve the pair of equations.
x + y = 5 and x - y = 2. Find x and y.

(2)

Solve the pair of equations by elimination, multiplying one equation first.
x + 2y = 8 and 2x + y = 7. Find x and y.

(3)

The sum of two numbers is 15. The larger number is 3 more than twice the smaller number. Find the two numbers.

(3)

Solve the pair of equations by elimination, multiplying both equations first.
3x + 2y = 16 and 2x + 3y = 19. Find x and y.

(4)

A cinema charges a pounds for an adult ticket and c pounds for a child ticket.
3 adult tickets and 2 child tickets cost £23 in total.
2 adult tickets and 5 child tickets cost £30 in total.
Form a pair of simultaneous equations and solve them to find a and c.

(4)

The pair x = 5, y = 1 is claimed to be a solution of x - y = 4. State whether this claim is true.

(1)

Given y = 2x, work out y when x = 6.

(1)

Given x + y = 9 and x = 5, work out y.

(1)

Given x - y = 3 and y = 5, work out x.

(1)

The pair x = 2, y = 6 is claimed to satisfy y = 3x. State whether this claim is true.

(1)

Solve the pair of equations by elimination.
x + y = 11 and x - y = 3. Find x and y.

(2)

Solve the pair of equations by elimination.
2x + y = 13 and x + y = 8. Find x and y.

(2)

Mark scheme · 2.17 Introduction to Simultaneous Equations

Question 1

(a) M1 correct elimination leading to 4y = 8 or equivalent
(a) M1 correct method to find y: y = 2
(a) A1 substitute to find x = 7/2 or 3.5 cao
(a) Answer: x = 7/2, y = 2

Question 2

(a) M1 rearrangement to get y = 3x - 7 and substitution into the second equation
(a) M1 correct algebra to a single equation in x, e.g. x + 2(3x - 7) = 4 giving 7x = 18
(a) A1 correct values x = 18/7 and y = 5/7 cao
(a) Answer: x = 18/7, y = 5/7

Question 3

(a) M1 multiply first equation by 3 to give 3x + 12y = 33 or equivalent
(a) M1 subtract the second equation correctly to find 14y = 32
(a) A1 y = 16/7 and x = 13/7 cao
(a) Answer: x = 13/7, y = 16/7

Question 4

(a) M1 correct multiplication to make a coefficient equal, e.g. multiply first by 3 and second by 4 to eliminate x producing 12x + 15y = 6 and 12x - 8y = 44
(a) M1 correct elimination to find 23y = -38 or equivalent
(a) M1 correct value for y, y = -38/23
(a) A1 substitute to find x = 59/23 cao
(a) Answer: x = 59/23, y = -38/23

Question 5

B1 Yes, because 3 + 4 = 7
Answer: Yes

Question 6

M1 substitute y = x + 1 into x + y = 9 to get x + (x + 1) = 9
A1 x = 4, y = 5 cao
Answer: x = 4, y = 5

Question 7

M1 substitute y = 2x - 1 into 3x + y = 14 to get 3x + 2x - 1 = 14, so 5x = 15
A1 x = 3, y = 5 cao
Answer: x = 3, y = 5

Question 8

M1 add the equations to eliminate y, e.g. 2x = 14
A1 x = 7, y = -3 cao
Answer: x = 7, y = -3

Question 9

M1 add the equations to eliminate y, e.g. 2x = 7
A1 x = 3.5, y = 1.5 cao
Answer: x = 3.5, y = 1.5

Question 10

M1 multiply the first equation by 2 to get 2x + 4y = 16
M1 subtract to eliminate x, e.g. 3y = 9
A1 x = 2, y = 3 cao
Answer: x = 2, y = 3

Question 11

M1 correct equations set up, e.g. n + (2n + 3) = 15 where n is the smaller number
M1 correct method to solve, e.g. 3n = 12
A1 4 and 11 cao
Answer: The numbers are 4 and 11

Question 12

M1 multiply the first equation by 3 and the second by 2, e.g. 9x + 6y = 48 and 4x + 6y = 38
M1 subtract to eliminate y, e.g. 5x = 10
M1 x = 2 found and substituted back correctly
A1 x = 2, y = 5 cao
Answer: x = 2, y = 5

Question 13

M1 correct equations formed: 3a + 2c = 23 and 2a + 5c = 30
M1 correct elimination method, e.g. multiply first by 5 and second by 2 to eliminate c
M1 a = 5 found
A1 a = 5, c = 4 cao
Answer: Adult ticket = £5, child ticket = £4

Question 14

B1 True, because 5 - 1 = 4
Answer: True

Question 15

B1 y = 12 cao
Answer: y = 12

Question 16

B1 y = 4 cao
Answer: y = 4

Question 17

B1 x = 8 cao
Answer: x = 8

Question 18

B1 True, because 3 x 2 = 6
Answer: True

Question 19

M1 add the equations to eliminate y, e.g. 2x = 14
A1 x = 7, y = 4 cao
Answer: x = 7, y = 4

Question 20

M1 subtract the equations to eliminate y, e.g. x = 5
A1 x = 5, y = 3 cao
Answer: x = 5, y = 3

Introduction to Simultaneous Equations - Worksheets, Questions and Revision

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2.17 Introduction to Simultaneous Equations

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