Chapter 6 test review Name: ________________ 1. Solving a system of two equations with two unknowns. This would be the equation of two lines. If they were in slope intercept form, the best way to solve for the system would be by graphing the two or by algebraic substitution. Lets try both. a. Graphing (by hand and by calculator) i. Y = 3x + 5 Y = -2x + 10 b. Algebraic substitution i. Y = -20x + 30 Y = -30x + 50 2. If a system of two equations with two unknowns is not in slope-intercept form it may be easiest to solve the system using elimination. Here are some examples where elimination would be the way to go. a. 3x + 3y = 12 -3x + 6y = 15 b. 2x – 3y = 3 3x + 4y = 13 3. After we learned all the previous methods we looked at using matrices and Guassian elimination to solve for systems of equations. Solve the following systems using matrices. Do the first by hand and you can use your calculator to solve the second one. a. 3x + 4y = 23 x + 3y = 11 b. 7x + 3y = 29 3x – 2y = 19 4. We know that in the real world things get more complicated than two equations and two unknowns, but we only go as far as three equations and three unknowns. Use either elimination or matrices to solve for the following system. You can use your calculator if you choose to solve the system using matrices. a. x + y + z = 3 x– y+z=3 2x + y + z = 4 5. Finally we looked at using matrices, not to solve systems of equations, but to store information. When we use matrices for storing information it is necessary that we know how to add, subtract, and multiply matrices. Use the following matrices to perform these operations if you can. If you can’t perform the given operation, explain why. A= B= C= D= a. A + B = b. A – B = c. –C = d. D * O(zero matrix) = e. A * C = f. C * D = g. A * B = 6. All this knowledge is great to know, but we need to be able to apply it somehow. Solve the following problems using the tools we learned in this chapter. a. The Copycat Toy Company has decided to create two new toys. One is called the CP1 while the other is called the CP2. Each CP1 requires 15 minutes of labor while each CP2 requires 30 minutes of labor. Plastic for each CP1 costs $2 while plastic for each CP2 costs $3. Yesterday the company spent $124 on plastic and used 18 hours of labor time in making new figures. How many of each toy was made yesterday? (You will need to use the fact that there are 60 minutes in an hour) b. A steel company makes 2 types of beams. One is an I beam while the other is a T beam. During 2002, the sales, in thousands of tons, for each quarter (3 month period) are given in the matrix below. During 2003, the matrix below gives the sales for each quarter. Write a matrix representing the total sales for each quarter during the two-year period. c. Happy Henry’s has two local drugstores in Wisconsin. Sales at both stores for January, February, and March in 1995 are given below for three types of aspirins – C(children’s aspirin), R(regular aspirin), and E(extra strength aspirin). Because of a cold winter in 1996, sales doubled at store A and tripled at store B. Write a matrix for total sales in 1996 for the three months. What matrix operations did you perform to answer this question?