Simultaneous Equations

Substitution

100

y = 3x + 1

y - 6x = 10

x = -3 , y = -8

200

y = -2x + 13

y - 4x = - 11

x = 4, y = 5

300

4x + 2y = -20

y = x - 4

x = -2, y = -6

400

5x - y = 21

y = -7x + 15

x = 3, y = -6

500

y = -8x - 3

8x + 4y = 12

x = -1, y = 5

Elimination 1

100

4x + 9y = 29

6x - 9y = 21

x = 5, y = 1

200

x + 5y = 13

x + y = -3

x = -7, y = 4

300

-8x - 5y = 18

8x + 7y = -22

x = -1, y = -2

400

-5x - 6y = 14 

3x - 6y = -18

x = -4, y = 1

500

x - 2y = -7

3x - 4y = -15

x = -1, y = 3

Factorise

100

Factorise 5x² + 15x

5x(x + 3)

200

Factorise 2(a + b) + 3c(a + b)

(2 + 3c)(a + b)

300

Factorise xy + 2x + 2y + 4

x(y + 2) + 2(y + 2)

= (x + 2)(y + 2)

400

Factorise x² + 3x - 18

(x + 6)(x - 3)

500

Factorise x² + 10x + 25

(x + 5)²

Inequalities

100

Solve 2x + 6 < 14

x < 4

200

Solve (x/9) + 6 < 4

x < -18

300

-x + 7 < 9

x > -2

400

5x + 2 > 8x - 4

x < 2

500

(1 + x)/2 < (x - 1)/3

x < -5

Word Problems

100

1 ruler and 2 pens cost $1.55

3 pens cost $1.20

How much does a ruler cost?

75c

200

3 songs and 5 films cost a total of $28 

3 songs and 2 films cost a total of $13

How much does each cost?

Songs = $1

Films = $5

300

Two numbers have a sum of 20 and a difference of 8. What are the numbers?

14 and 6

400

Paul collects baseball cards and football cards. The number of baseball cards is 10 more than twice the number of football cards. In total, Paul has 70 cards. How many of each type card does Paul have?

20 Football cards

50 Baseball Cards

500

Mayfield High School sold tickets for a school musical. Seats in the auditorium cost $6 each and balcony seats cost £4. A total of 200 tickets was sold and $960 was collected. How many of each type of ticket was sold?

120 Balcony Seats

80 Auditorium Seats