State whether x = 3, y = 4 satisfies the equation x + y = 7.
(1)
2
The pair x = 5, y = 1 is claimed to be a solution of x - y = 4. State whether this claim is true.
(1)
3
Given y = 2x, work out y when x = 6.
(1)
4
Given x + y = 9 and x = 5, work out y.
(1)
5
Given 2x = 14, work out x.
(1)
6
Given x - y = 3 and y = 5, work out x.
(1)
7
The pair x = 2, y = 6 is claimed to satisfy y = 3x. State whether this claim is true.
(1)
8
Solve the pair of equations by elimination. x + y = 11 and x - y = 3. Find x and y.
(2)
9
Solve the pair of equations by elimination. 2x + y = 13 and x + y = 8. Find x and y.
(2)
10
Solve the pair of equations by substitution. y = x + 1 and x + y = 9. Find x and y.
(2)
11
Solve the pair of equations by substitution. y = 2x - 1 and 3x + y = 14. Find x and y.
(2)
12
Solve the pair of equations by elimination. x + y = 4 and x - y = 10. Find x and y.
(2)
13
Solve the pair of equations. x + y = 5 and x - y = 2. Find x and y.
(2)
14
Solve the pair of equations by elimination, multiplying one equation first. x + 2y = 8 and 2x + y = 7. Find x and y.
(3)
15
Two numbers, x and y, satisfy x + y = 20 and x - y = 4. Find x and y.
(3)
16
The sum of two numbers is 15. The larger number is 3 more than twice the smaller number. Find the two numbers.
(3)
17
Solve the pair of equations by elimination, multiplying both equations first. 3x + 2y = 16 and 2x + 3y = 19. Find x and y.
(4)
18
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 pounds in total. 2 adult tickets and 5 child tickets cost 30 pounds in total. Form a pair of simultaneous equations and solve them to find a and c.
(4)
19
Stretch. The larger of two numbers exceeds the smaller by 6. Twice the smaller number plus three times the larger number equals 58. Find both numbers.
(4)
Mark scheme · KS3.M-A17D Introduction to Simultaneous Equations: Fluency and Exam Drill
Question 1
B1 Yes, because 3 + 4 = 7
Answer: Yes
Question 2
B1 True, because 5 - 1 = 4
Answer: True
Question 3
B1 y = 12 cao
Answer: y = 12
Question 4
B1 y = 4 cao
Answer: y = 4
Question 5
B1 x = 7 cao
Answer: x = 7
Question 6
B1 x = 8 cao
Answer: x = 8
Question 7
B1 True, because 3 x 2 = 6
Answer: True
Question 8
M1 add the equations to eliminate y, e.g. 2x = 14
A1 x = 7, y = 4 cao
Answer: x = 7, y = 4
Question 9
M1 subtract the equations to eliminate y, e.g. x = 5
A1 x = 5, y = 3 cao
Answer: x = 5, y = 3
Question 10
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 11
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 12
M1 add the equations to eliminate y, e.g. 2x = 14
A1 x = 7, y = -3 cao
Answer: x = 7, y = -3
Question 13
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 14
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 15
M1 add the equations to eliminate y, e.g. 2x = 24
M1 correct value x = 12 found
A1 x = 12, y = 8 cao
Answer: x = 12, y = 8
Question 16
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 17
M1 multiply the first equation by 3 and the second by 2, e.g. 9x + 6y = 48 and 4x + 6y = 38