Do all work on your own paper. Show your steps .
1. Solve the system of equations by graphing. State whether there is a unique
solution, no
solution, or an infinite number of solutions . If the answer is unique, express
it as an ordered
pair.
x + y = –7
4x – y = –8
2. Solve the system of equations by graphing . State whether there is a unique
solution, no
solution, or an infinite number of solutions. If the answer is unique, express
it as an ordered
pair.
y = x + 1
3y – 3x = 6
3. Solve the system of equations by substitution. State whether there is a
unique solution, no
solution, or an infinite number of solutions. If the answer is unique, express
it as an ordered
pair.
y = 2x – 13
4x + 9y = –7
4. Solve the system of equations by substitution. State whether there is a
unique solution, no
solution, or an infinite number of solutions. If the answer is unique, express
it as an ordered
pair.
4x = 2y + 6
y = 2x – 3
5. Solve the system of equations by the addition method . State whether there is
a unique
solution, no solution, or an infinite number of solutions. If the answer is
unique, express it as
an ordered pair .
2x – 5y = 23
3x + 5y = –28
6. Solve the system of equations by the addition method .
State whether there is a unique
solution, no solution, or an infinite number of solutions. If the answer is
unique, express it as
an ordered pair.
–3x – 5y = 7
5x + 4y = 10
7. During a public ice skating session, an ice skating arena charged an
admission fee for each
child plus a rental fee for each pair of ice skates. Byron Carter paid the
admission fees for his
5 nephews and rented 4 pairs of ice skates. He was charged $37.75. Corrina
Prescott paid the
admission fees for her 4 grandchildren and rented 2 pairs of ice skates. She was
charged
$26.00. What was the admission fee? What was the skate rental fee?
8. A solution of 48% pesticide is to be mixed with a solution of 34% pesticide
to form 56 liters
of a 44% solution. How many liters of the 48% solution must be used?
9. A store is having a sale on sweaters. A crew neck sweater sells for $24 and a
V-neck sweater
sells for $18. If they sold 38 sweaters in one day, and took in $786.00, how
many of each
type of sweater were sold?
10. The sum of the measures of the angles of a triangle is 180 degrees. The
largest angle
measures 100 less than the sum of the other two. The measure of the middle-sized
angle is
the average of the other two. Find the measures of the three angles.
11. Alex is developing film in his darkroom when he realizes that he does not
have the proper
developer. He needs a mixture that is 20% developer but he only has a mixture
that is 60%
developer and another that is 10% developer. How much of the 10% developer and
how
much of the 60% developer must be mixed to produce 8 pints of the mixture he
needs?
12. How much water should be added to 20 milliliters of a 30% hydrochloric acid
solution in
order to dilute it to a 10% strength HCl solution?
13. Steve Fletcher wants to design a walkway to his house using two different
kinds of paving
bricks. He finds the job will require 380 bricks. The home improvement store
sells two
kinds of paving bricks that will work together, a red brick variety which sells
for $5.00 per
unit and a cement brick which sells for $3.00 per unit. How many of each type of
brick
should he buy if he has budgeted $1500 for the project?
14. A plane flies 560 mi. in 1.75 hr. traveling with the wind. The return trip
later against the
wind takes the plane 2 hr. Find the speed of the plane and the speed of the
wind. Let x =
the speed of the plane and y = the speed of the wind.
15. Rachelle does tutoring and paper grading for the math
department. One week she tutored
for 7 hours and graded for 8 hours and made $107.00. The following week she
tutored for
10 hours and graded for 6 hours and made $123.00. How much does she make per
hour
tutoring and how much per hour grading?
16. A theater has an orchestra section and a balcony section. At one
performance, the sale
of 95 orchestra seats and 75 balcony seats generated a revenue of $4975. At a
later
performance, the sale of 60 orchestra seats and 135 balcony seats brought in
$5070.
Find the cost of an orchestra seat and the cost of a balcony seat.
17. Simplify and write without negative exponents : –3a–3b
18. Simplify and write without negative exponents: 3x–1y
19. Evaluate each expression:
20. Simplify and write without negative exponents:
21. Simplify and write without negative exponents:
22. Add:
23. Subtract :
24. Subtract:
from
25. Perform the indicated operations:
26. Multiply :
27. Multiply:
28. Multiply: (4x – 3y)(4x + 3y)
29. Expand and simplify : (3a – 2b)2
30. Use long division to divide : 4x2 + 2x – 15
by 2x + 5
31. Divide:
32. Divide:
33. a. Find the greatest common factor of
b. Factor the greatest common factor from
34. a. Find the greatest common factor of
b. Factor the greatest common factor (with a negative
coefficient) from
35. Factor completely. If an expression cannot be factored
with rational numbers, write
“Prime.”
