How addition-multiplication used to solve a linear equation

Question

Assignment: Discussion Questions:

How are addition and multiplication used to solve a linear equation?  Demonstrate by solving "15x + 7 = 31 + 3x"Translate the following into a system of equations, then solve it:A customer walks into an electronics store and buys five MP3 players and eight sets of headphones, paying $840.  A second customer buys three MP3 players and four sets of headphones, and pays $480.  How much does an MP3 player cost?  How much does a set of headphones cost?

1. 1.  (i) What are the x-intercept and y-intercept of a linear equation? 

(ii) What are their coordinates on a graph? 

(iii) How can they be used to graph a line? 

(iv) Demonstrate by determining the intercepts of "14x + 7y = 21". 

1.  
   1. Write a system of equations having
      1. A unique solution.
      2. An infinite number of solutions.
      3. No solution.

How would each system appear graphically?

1.  
   1. Explain how to apply elimination in solving a system of equations.
      1. Explain how to apply substitution in solving a system of equations.
      2. Demonstrate each technique in solving the system

3x + 9y = 12

5x - 4y = 3

6: Linear Equations and their Solutions

From the given polynomials, identify the polynomials of degree one.

1. 311y - 5 - 43y
2. (11y²)^1/2 + 14
3. 10 + (19)^1/2x
4. 2 + 15x
5. 52y⁴ + 7x + 2
6.  (68)¹y¹
7. x³ + 3x - 9
8. (2x)^1/2 + 4x - 8

Solve the following:

1. 1. -2x = 3x + 4
   2. ^3x/₄ = 6
   3. ^y/₆ + 1 = 9
   4. 6 = -^2x/₄
   5. Find f(1) for f(x) = 4x³ - 3x² - x + 2
   6. A function gives the value of C as 2 × (²²/₇) × r. Find C when r = 21 cm and r = 84 cm.

7: Ratio and Proportion

1. A lawyer bills her clients $200 per hour of service. If a client's case requires 39 hours to complete, use proportion to calculate how much the client will owe the lawyer (excluding tax).

2. A new virus is released on the internet; the administrator of a department's Local Area Network ( LAN) is given five minutes by a manager to estimate the impact. The administrator samples 15 of the PCs connected to the LAN, and finds that 9 are infected; use proportion to estimate the number of infected PCs if there are a total of 202 PCs connected to the LAN.

3. An administrator of a popular web site is told that a new server can handle 41,000 "hits" (users accessing the site) per second. The web site currently experiences a peak demand of about 105,000 hits per second; but every month, the peak demand increases by 2800 hits per second. Use a proportion equation to determine how many new servers the administrator should buy to address expected traffic for the next 24 months.

8: Graph and Analyze Linear Functions

1. How do we write the equation of a horizontal line?  What would be an example?
2. How do we write the equation of a vertical line?  What would be an example?
3. The points (3, 9), (5, 13), (15, 33), (34, 71), (678, 1359), and (1234, 2471) all lie on line M.
   The points (3, -9), (5, -11), (15, -21), (34, -40), (678, -684), and (1234, -1240) all lie on line N.
   1. Form the equations of both the lines.  Show your work. 
   2. What are the co-ordinates of the point of intersection of lines M and N?
   3. Write the co-ordinates of the intersections of lines M and N with the x-axis.
   4. Write the co-ordinates of the intersection of lines M and N with the y-axis.

9: Solving System of Linear Equations

1. Solve by substitution or elimination method:
             3x -  2y = 8
             -12x + 8y = 32

2. Solve by substitution or elimination method:

        7x - 5y = 14
             -4x + y = 27

3. Solve by substitution or elimination method:
             -4x + 3y = 5
              12x - 9y = -15

10: Graphical Representation of Linear Equations

1. Plot the graph of the equations 3x - 8y = 5 and 4x - 2y = 11 and interpret the result.
2. Plot the graph of the equations 4x - 6y = 2 and 2x - 3y = 1 and interpret the result.
3. Plot the graph of the equations 10x - 4y = 3 and 5x - 2y = 6 and interpret the result.