Question: Describe the various methods of solving linearsystems. With which method of solving linear systems are you mostcomfortable, and why?
Hint: First, define a linear system, and give an example. Then,discuss the methods, and show the steps to solve your example.Finally, talk about advantages and drawbacks of each method.
\"Real-Life\" Relationship: Any relationship where we have a fixedcost and variable cost can be represented by a linear equation.
For instance, the cost of a rental car from Hertz might be $100plus $0.70 per mile, while Enterprise might charge $80 plus $0.80per mile. We can solve the following system to find out when thecost is the same (c = cost, m = miles driven)
c = 0.7m + 100 (Hertz)
c = 0.8m + 80 (Enterprise)
It turns out that they are equal when the mileage is m =200.
Challenge 1: Given two lines in standard form, how can youquickly decide if they have the same slope, simply by using ratiosof y and x coefficients?
Challenge 2: What is a quick way (without finding the slope orsolving for y) to decide whether the following system has asolution?
2x + 3y = 4
2x + 3y = 5
