1. Use the substitution method to find all solutions of the system of equations {image} Choose the answer from the following:
(5, 25), ( - 4, 16)
( - 5, 25), (4, 16)
(5, 16), ( - 4, 25)
(4, 16), ( - 4, 16) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

2. Find all solutions of the system of equations {image} Choose the answer from the following:
(7, - 42), (10, - 30)
(14, - 84), (20, - 60)
(10, 42), (7, 30)
( - 7, 42), (7, - 30) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

3. 1,700 children, 2,500 adults 2,500 children, 1,700 adults
The admission fee at an amusement park is $2 for children and $4 for adults. On a certain day, 4,200 people entered the park, and the total admission fees collected were $13,400. How many children and how many adults were admitted? Choose the correct answer from the following:
1,700 children, 2,500 adults
2,500 children, 1,700 adults
1,700 children, 2,400 adults
2,000 children, 2,500 adults 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

4. Use back - substitution to solve the triangular system. {image}1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

5. An investor has $100,000 to invest in three types of bonds: short-term, intermediate-term, and long-term. Short-term bonds pay 5% annually, intermediate-term bonds pay 6%, and long-term bonds pay 7%. The investor wishes to realize a total annual income of 6.1%, with equal amounts invested in short- and intermediate-term bonds. How much should she invest in each type to satisfy the given conditions? 1.
{image} 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

6. Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. {image} Select the correct answer.
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

7. 15 ml. 10% acid, 81.25 ml. 20% acid, 3.75 ml. 40% acid
A chemist has three acid solutions at various concentrations. The first is 10% acid, the second is 20%, and the third is 40%. How many milliliters of each should he use to make 100 mL of 19.25% solution, if he has to use 4 times as much of the 10% solution as he does of the 40% solution? Select the correct answer from the following:
15 ml. 10% acid, ml. 20% acid, 3.75 ml. 40% acid
81.25 ml. 10% acid, 3.75 ml. 20% acid, 15 ml. 40% acid
3.75 ml. 10% acid, 15 ml. 20% acid, ml. 40% acid 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

8. Solve a matrix equation for x and y: {image} Select the correct answer.
x = -4, y = 5
x = 5, y = -4
x = -4, y = -21
x = -5, y = 5
x = -4, y = 6 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

9. Find the inverse of the matrix
Find the inverse of the matrix. {image} Choose the answer from the following:
{image} 1. 2. 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

10. Find the inverse of the matrix. {image}1. 2.
{image} 3. 4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

11. Evaluate the determinant
Evaluate the determinant. Use row or column operations whenever possible to simplify your work. {image} Choose the answer from the following:
D = 14,580
D = - 14,581
D = 0
D = 35 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

12. Solve for x: {image} Choose the answer from the following:
x = 0, x = 5, x = 7
x = 5, x = 7
x = - 5, x = - 7
x = 12, x = 5, x = 7 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

13. Solve the system of inequalities
Solve the system of inequalities. {image} Choose the graph of the correct solution from the following:
{applet} 1. 2. 3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50