1. When using the elimination or substitution method to solve a system of linear equations, how can you tell if a system of linear equations has no solution? What is the relationship between the graphs of the equations?

2. What is a quadratic function? Give an example and describe where a quadratic model might be used.

3. Suppose that the total weekly cost for the production and sale of x bicycles is C(x) = 23x + 3420 dollars and that the total revenue is given by R(x) = 89x dollars, where x is the number of bicycles.

a) Write the equation of the function that models the weekly profit from the production and sale of x bicycles.

b) What is the profit on the production and sale of 150 bicycles?

4. Consider the equationx⁴+6x²+2=0 has no rational zeroes. a. Explain why this equation has no rational zeros. b. Is this the same question as asking why this equation has no real roots? Why or why not? c. Give another example of a polynomial equation that has no real roots and describe how you obtained the equation.