1) System 3x-y=-9 and x+2y=2 may be solved algebraically by using several different methods. Illustrate the first step in solving system using each method below.
a. Substitution for y
b. Elimination of x
2. Tell how many solutions there are for the system of linear equations whose graph is explained below. Ensure to describe/justify your answer.
a. Pair of parallel lines
b. The single line
c. Pair of lines which are not parallel
3. The student proposed following method of sketching solution to the system of two inequalities. First, shade region of points which satisfies first inequality. Then, shade region of points which satisfy second inequality. Solution consists of all points which have been shaded. Do you agree? Describe. Support the answer using system 5x-3y>1 and 3x+4y less than or equal to 18.
3. Congratulations! You have now been hired as the manager of to, a small business which makes frozen pizzas to sell at local markets. Owner gave you following information:
o Preparation and packaging takes 0.2 hours for every box of 12-inch pizzas and 0.25 hours for every box of 16-inch pizzas.
o You can pay staff for no more than 240 hours of labor each week.
o The staff must meet the company quota of producing at least 1,000 boxes of pizza per week.
Let x represent number of 12-inch pizzas made and let y represent number of 16-inch pizzas made.
a. Write the inequality for each constraint.
b. Graph feasible region which represents constraints in (a).
c. Locate and label vertices for feasible region.
d. Write down objective function.
e. Determine number of every kind of pizza made which will maximize profit.