Simultaneous Equations Quiz

Question 1

Solve: x + y = 7 and x − y = 3

Accepted Answer

x = 5, y = 2

Answer

x = 4, y = 3

Answer

x = 3, y = 4

Answer

x = 2, y = 5

Question 2

Solve: 2x + y = 10 and x + y = 6

Accepted Answer

x = 4, y = 2

Answer

x = 3, y = 4

Answer

x = 2, y = 4

Answer

x = 5, y = 0

Question 3

What does it mean graphically when two linear simultaneous equations have no solution?

Accepted Answer

The lines are parallel and never meet

Answer

The lines cross at the origin

Answer

The lines are the same line

Answer

The lines are perpendicular

Question 4

Solve by substitution: y = 2x + 1 and 3x + y = 16

Accepted Answer

x = 3, y = 7

Answer

x = 4, y = 9

Answer

x = 5, y = 11

Answer

x = 2, y = 5

Question 5

Solve: 3x + 2y = 12 and x − y = 1

Accepted Answer

x = 14/5, y = 9/5

Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 4, y = 0

Question 6

Solve by elimination: 4x + 3y = 21 and 2x − 3y = 3

Accepted Answer

x = 4, y = 3

Answer

x = 4, y = 5/3

Answer

x = 3, y = 3

Answer

x = 2, y = 3

Question 7

A cinema sells adult tickets for £9 and child tickets for £5. 50 tickets are sold for a total of £330. How many adult tickets were sold?

Accepted Answer

20

Answer

15

Answer

25

Answer

30

Question 8

Solve: 5x + 2y = 16 and 3x + 2y = 12

Accepted Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 1, y = 5

Answer

x = 4, y = −2

Question 9

How many solutions do simultaneous equations have if the two lines are identical (same equation)?

Accepted Answer

Infinitely many

Answer

None

Answer

Exactly one

Answer

Exactly two

Question 10

Solve the simultaneous equations: y = x² and y = x + 2

Accepted Answer

x = 2 or x = −1

Answer

x = 1 or x = 2

Answer

x = −2 or x = 1

Answer

x = 0 or x = 2

Question 11

Solve: 2x + 5y = 19 and 2x + 3y = 11

Accepted Answer

x = −2, y = 5

Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 1, y = 4

Question 12

Solve: x + 2y = 8 and 3x − y = 3

Accepted Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 1, y = 3

Answer

x = 4, y = 2

Question 13

Two numbers sum to 15 and their difference is 3. What are the numbers?

Accepted Answer

9 and 6

Answer

10 and 5

Answer

8 and 7

Answer

12 and 3

Question 14

Solve: 4x − y = 5 and 2x + 3y = 13

Accepted Answer

x = 2, y = 3

Answer

x = 3, y = 2

Answer

x = 1, y = −1

Answer

x = 2.5, y = 5

Question 15

The sum of two numbers is 20 and one is three times the other. What is the smaller number?

Accepted Answer

5

Answer

4

Answer

6

Answer

8

Question 16

Solve: 3x + 4y = 24 and 6x − 4y = 12

Accepted Answer

x = 4, y = 3

Answer

x = 6, y = 1.5

Answer

x = 3, y = 4

Answer

x = 2, y = 4.5

Question 17

Which method is best when one equation already has y isolated (e.g. y = 3x − 1)?

Accepted Answer

Substitution

Answer

Elimination

Answer

Graphical method

Answer

Trial and improvement

Question 18

Solve: 5x + y = 14 and y = 2x

Accepted Answer

x = 2, y = 4

Answer

x = 3, y = 6

Answer

x = 1, y = 2

Answer

x = 4, y = 8

Question 19

Solve simultaneously: x + y = 5 and x² + y² = 13

Accepted Answer

x = 2, y = 3 or x = 3, y = 2

Answer

x = 4, y = 1 or x = 1, y = 4

Answer

x = 5, y = 0 or x = 0, y = 5

Answer

x = −2, y = 7

Question 20

Solve: 7x − 3y = 22 and 5x + 3y = 26

Accepted Answer

x = 4, y = 2

Answer

x = 3, y = −1/3

Answer

x = 5, y = 3

Answer

x = 2, y = −8/3