MAT 103 F09 TEST 3 REVIEW (CH 4-5)

Transcription

1 MAT 103 F09 TEST 3 REVIEW (CH 4-5) NAME For # 1-3, solve the system of equations by graphing. Label the equation of each line on your graph and write the solution as an ordered pair. Be sure to CHECK your solution in both of the original equations. 1) 2x - y = 4 y = 2 2) -1 +2x = -9 2x + y = -2 1

2 Solve the system of equations by graphing. Label the equation of each line on your graph and write the solution as an ordered pair. Be sure to CHECK your solution in both of the original equations. 3) 3x + y = 7 2x - y = 8 4) Use a graphing calculator to solve the system 2x-3y=12. Give the answer to three decimal places. 5x + y = -2 Complete each part of the following problem. 5) A company that manufactures laser printers for computers has monthly fixed costs of $177,000 and variable costs of $650 per unit produced. The company sells the printers for $1,250 per unit. Let x represent the number of laser printers produced and sold each month. a) Write the equation for the total monthly cost of producing x printers: C = b) Write the equation for the revenue made by selling x printers: R = c) Using your calculator, graph the cost and revenue functions in the same viewing window. d) Write the coordinates of the break-even point: e) Determine the number of printers that must be produced and sold each month for the company to break even? Write out your anwer in sentence form. f) Write the equation of the Profit function, P(x). P(X) = g) Use the graph of the profit function to determine the number of printers that must be produced and sold in order to make a profit. 2

3 6) A system of linear equations that has at least one solution is called a(n) system. 7) A system composed of two dependent linear equations has solutions. 8) Describe the graph of an inconsistent system of two linear equations. 9) Sketch the graph of a consistent system of two independent linear equations. For # 10-12, solve the system of equations by SUBSTITUTION. Write the answer as an ordered pair on the answer blank below. CHECK your solution in both original equations. If there is no solution, state this. 10) x - 7y = -35 7x - 6y = -30 3

4 11) -2x + 4y = 9 x - 2y = -3 12) 3x + 2y = 0 6x + 2y = 5 4

5 For # 13-14, solve the system of equations by ELIMINATION. Write the answer as an ordered pair on the answer blank below. CHECK your solution in both original equations. If there is no solution, state this. 13) 2x + y = 34 6x - y = 6 14) 2x + 5y = 13 5x + 3y = 23 5

6 15) Solve the system of equations using either substitution or elimination. x = 5y - 3-3x + 15y = 9 Solve this system using ALGEBRAIC METHODS. Write the answer out in words. 16) Suppose that the supply and demand equations for a logo sweat shirt in a particular week are p = q, for the demand equation; and p = 0.20q + 25, for the supply equation. Find the equilibrium price and quantity. Provide an appropriate response. 17) Given matrix A: A = What is the size of A? 18) Write the augmented matrix for the system. Do NOT solve the system. 8x 1 + 9x 2 = 117 4x 1 + 6x 2 = 66 6

7 Write a system of equations in x, y, and z associated with the augmented matrix ) For # 20-23, set up an augmented matrix and then solve the system by finding the reduced row-echelon form of the matrix (using your graphing calculator). State the answer as an ordered pair or ordered triple. If the system has no solution or infinitely many solutions, so state. 20) 0.4x x2 = x1-0.3x2 = ) 7x - y + 3z = 18 7x + 3y + 3z = 50-2x - 4y + z = ) 8x - 5y = -6-8x + 5y = 8 7

8 23) x + y + z = 3 x - y + 3z = 7 3x + y + z = -3 For # 24-25, set up a system of three linear equations to model the problem. Solve this system using matrices on your graphing calculator. Write out your answer in sentence form. 24) A $124,000 trust is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400 annual income from the investments, how much should the bank invest in each? Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages. 25) A theater has 1200 seats that are divided into three sections: orchestra, mezzanine, and balcony. Each seat sells for $65 in the orchestra sections, $48 each in the mezzanine, and $35 each in the baclony section. There are 150 more baclony seats than mezzanine seats. If all of the seats are sold out, the theater will bring in $55,640 in revenue. Find the number of seats in each section of the theater. 8

9 For # 26-28, graph the inequality. SHOW ALL WORK NEATLY. Use a straightedge to graph the boundary line. Label the equation of the boundary line and indicate the test point used. 26) 4x + y 3 Graph the inequality. 27) 4x - 2y 8 28) -5y >

10 For # 29-31, graph the solution set of the system of linear inequalities. SHOW ALL WORK NEATLY. Use a straightedge to graph the boundary lines. Label the equation of the boundary line and clearly indicate the solution region. 29) y -3x - 3 y x + 8 Graph the solution set of the system of linear inequalities. 30) y > 2 x 5 31) x -4 y > 2 3x + y < 6 10

11 Graph the system of inequalities and find the coordinates of the corner points of the solution region for: 3x + 2y 54 32) 4x + 5y 100 x 0 y 0 Hint: For equations 1 and 2, find the x-intercept and y-intercept and use the intercepts to graph each boundary line. Corner Points: 11