project 6 pre calc

Take this test as you would take a test in class. After you are finished, check your work against the answers given in the back of the book. In Exercises 1-3, solve the system by the method of substitution. Check your solution graphically. 1. J x - y=6 3. [4x - yz = 7 13x + 5y = 2 2. y = x - 1 x - y = 3 In Exercises 4-6, solve the system by the method of elimination. 4. [2x + 5y = -11 5. 3x - 2y + 2 = 0 6. x - 4y - 2= 3 5x - y = 19 6x + 2y + 3z = -2 2x - 5y + = = 0 3x - 4y + 5z = 5 3x - 3y + 2z = -1 7. Find the equation of the parabola y = ax + bx + c that passes through the points (0, 6), (-2, 2), and (3, =). In Exercises 8 and 9, write the partial fraction decomposition for the rational expression. -2x + 2y + 3z = 7 8. - 3.x - 2 x - y = -5 (x - 1)2 y + 4: = -1 In Exercises 10 and 11, use matrices to solve the system of equations, if possible. System for 13 10. (2x + y + 2z = 4 11. (2x + 3y + z = 10 2x + 2y = 5 2x - 3y - 3z = 22 2x - y + 62 = 2 (4x - 2y + 32 = -2 12- (4, 11) 10- 12. If possible, find (a) A - B, (b) 3A. (c) 3A - 28, and (d) AB. 8- 6 (4, 5) 4 - (-1, 1) -8 -6 -4 -2 2 4 6 13. Find A-' for A = - 1 O and use A- to solve the system at the right. (-1,-5) -6+ In Exercises 14 and 15, find the determinant of the matrix. Figure for 16 14. - 25 -71 15. - . - 8 NN 400 - 600 16. Use determinants to find the area of the parallelogram shown at the right. 17. Use Cramer's Rule to solve (if possible) 2x - 2y = 3 * + 4y = -1' 300 - 100 18. The flow of traffic (in vehicles per hour) through a network of streets is shown at the X5 right. Solve the system for the traffic flow represented by x; / = 1, 2, 3, 4, and 5. Figure for 18