Practice Test - Chapter 3. Solve each system of equations by using either substitution or elimination.
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1 Solve each system of equations by using either substitution or elimination Substitute x + 4 for y in the second equation and solve for x. Multiply the first and the second equation by 4 and 5 then add. Substitute 8 for x in the first equation and solve for y. Substitute 8 for y in the second equation and solve for x Multiply the first equation by 2 and add with the second equation. Multiply the first and the second equation by 5 and 3 respectively then add. Substitute 1 for y in the second equation and solve for x. Substitute 2 for x in the second equation and solve for y. 5. MULTIPLE CHOICE Which graph shows the solution of the system of inequalities? esolutions Manual - Powered by Cognero Page 1
2 Solve each system of inequalities by graphing. 6. A B 7. C D 8. Graph the inequalities. Option B is the correct answer. esolutions Manual - Powered by Cognero Page 2
3 9. price for each pedicure is $45, the function that represents her daily income is I(m, p ) = 185m + 45p. Sierra can only do a whole number of manicures and pedicures so substitute (0, 0), (0, 5), (9, 5), and (18, 0) in the income function to determine the maximum. 10. SALONS Sierra King is a nail technician. She allots 20 minutes for a manicure and 45 minutes for a pedicure in her 7-hour word day. No more than 5 pedicures can be scheduled each day. The prices are $18 for a manicure and $45 for a pedicure. How many manicures and pedicures should Ms. King schedule to maximize her daily income? What is her maximum daily income? Let m represent the number of manicures and p represent the number of pedicures. Write the system of constraints for the scenario. Since she cannot do a negative procedure, both variables must be greater than or equal to 0. 0 p 5 m 0 20m + 45p 420 Graph the system of inequalities and find the vertices of the feasible region. The maximum income will be produced when she schedules 9 manicures and 5 pedicures. This will produce a maximum income of $ COLLEGE FOOTBALL In a recent year, Darren McFadden of Arkansas placed second overall in the Heisman Trophy voting. Players are given 3 points for every first-place vote, 2 points for every secondplace vote, and 1 point for every third-place vote. McFadden received 490 total votes for first, second, and third place, for a total of 878 points. If he had 4 more than twice as many second-place votes as third-place votes, how many votes did he receive for each place? Let x, y and z be the number of first, second and third place vote. The system of equations represent this situation is: Substitute 2y + 4 for z in the first and second equation and simplify. The vertices of the feasible region are (0,0), (0, 5), (9.75, 5), and (21, 0). Since the price for each manicure is $18 and the Multiply the fourth equation by 3 and add with the esolutions Manual - Powered by Cognero Page 3
4 fifth equation. Perform the indicated operations. If the matrix does not exist, write impossible. 12. Substitute 147 for z in the fourth equation and solve for x. Distribute the scalar. Substitute 147 for z in the third equation and solve for y. Add corresponding elements. Therefore, he received 45 first-place, 298 secondplace and 147 third-place votes. 13. esolutions Manual - Powered by Cognero Page 4
5 Find the inverse of each matrix, if it exists. det (A) = The inner dimensions are not equal. So, the matrix subtraction is impossible MULTIPLE CHOICE What is the value of? F 44 G 44 det (A) = 3 H J 19. Therefore, option F is the correct answer. det (A) = 0 The value of the matrix is zero. So the inverse does not exist. esolutions Manual - Powered by Cognero Page 5
6 20. Cramer s Rule. Let C be the coefficient matrix of the system det (A) = 0 The value of the matrix is zero. So the inverse does not exist. Use Cramer s Rule to solve the following system of equations x y = 9 x + 2y = 8 Cramer s Rule. Let C be the coefficient matrix of the system The solution of the system is. if.. The solution of the system is if. Therefore, the solution of the system is ( 2, 5). 22. x y + 2z = 0 3x + z = 11 x + 2y = 0 esolutions Manual - Powered by Cognero Page 6
7 Therefore, the solution of the system is (4, 2, 1). esolutions Manual - Powered by Cognero Page 7
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Simplify each expression. 1. 2. 3. esolutions Manual - Powered by Cognero Page 1 4. 5. esolutions Manual - Powered by Cognero Page 2 6. 7. esolutions Manual - Powered by Cognero Page 3 8. 9. Identify the
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