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.Get Gains Gym offers a membership for a flat fee of $40 plus $4 per visit. BadLife Fitness offers their membership for a flat fee of $60 plus $2 per visit. How many visits per month is the total cost the same for both gyms?

 

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
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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