Solving Problems Involving Linear Systems
Set up and solve a linear system for the of the following question. Use ‘let’ statements to define the variables you will be using.
Show ALL of your work

1. Lukas is selling baseball caps to raise money for his school. The supplier charges a $110 design fee plus $4 per hat. Lukas wants to sell the hats for $8 each. How many hats does Lukas need to sell in order to break even?

Modelling Linear Equations 
Set up and solve a linear equation for each of the following questions. Use ‘let’ statements to define the variables you will be using and show ALL of your work when solving.
a) A number added to 10 is 14
b) Three times a number is equal to -2
c) The difference between a number and 8 is 12
d) Twice a number subtracted from 10 is equal to 8
e) A quarter of a number added to five is nine
f) If you take Mr. Webb’s age and multiply it by 3 and divide by 9 you get 9. How old is Mr. Webb?
g) If you take Mr. Webb’s favourite number, divide it by 3 and add 16, the result is 19. What is Mr. Webb’s favourite number?
h) Multiplying a number by 3 and subtracting 6 is the same as multiplying the number by 2 and adding 5. What is the number? 

 Solving Linear Systems by Substitution 
Solve the following systems of linear equations and clearly state what the
point of intersection is
Show ALL of your work

a) 3 x+ y=7
−x+2 y=7

b) y=7 x+3
x−y=3

c) 2 x+3 y=8
x−2 y=−3

        Solving Linear Systems by Substitution 
Solve the following systems of linear equations and clearly state what the point of intersection is
Show ALL of your work

5x − y = −4
2x − 3y = 1