Year 12 General Maths - Modelling with Linear Relationships

Solving Linear Equations

100

64 - 3x = 25

x = 13

200

6x + 7 = 5 - 2x

-0.25 or - 1/4

300

5(2x - 4) = 4

x = 12/5 or 2.4

400

1/3(2x + 1) = 5

x = 7

500

(x+1)/4 + (x+2)/5 = 2

x = 3

Simultaneous Equations

100

y = 3x + 2

y = x - 2

x = -2

y = -4

200

y = x - 1

2x + 3y = 12

x = 3

y = 2

300

y = -2x + 5

y = -2x - 1

The lines are parallel so there are no solutions

400

x - 1/4y = -2

y = 4x + 8

The lines are the same so there are infinitely many solutions

500

3x - y = 5

4x + y = 9

x = 2

y = 1

Graphing from Equations

100

What is the slope of the line y = 1/2x + 1

m = 1/2

200

What is the y-intercept of the line y = -2x + 5

y = 5

300

What is the slope of the line 3x + 2y = 12

m = -3/2

400

What is the x-intercept of the line 4x - y = 8

x = 2

500

Calculate the slope of the following line

-1/2