Name: ________________________________________ Date: ______________________ HR: ______
Algebra 2/Trig
Chapter 3 Review
Graph the system. Then classify the system as inconsistent, dependent, or independent. Then find the
solution from the graph if possible.
1.)
y = 2x + 3
4x – 2y = 4
2.)
2x + 4y = 16
y+2=x
3.)
Graph the linear inequality: 3𝑥 + 2𝑦 ≤ 6
1
4.)
Determine which ordered pair (x, y) is a solution of 2x – y ≤ 0.
A. (6, 1)
B. (1, 6)
C. (2, -6)
D. (3, -4)
Write the pair of parametric equations as a single equation in x and y.
𝑥(𝑡) = 𝑡 + 3
𝑦(𝑡) = 3𝑡
5.)
{
6.)
{
𝑥(𝑡) = 2 − 3𝑡 2
1
𝑦(𝑡) = − 3 𝑡
Write the system of inequalities whose solution is graphed as the shaded region.
7.)
8.)
2
Solve by any method: i.e. Substitution, Elimination.
9.)
10.)
11.)
y = 5x + 12
y = -3x + 4
x + y + 3z = 12
2y + 1 = 7
2x + 3y + 6z = 7
𝑦 ≤ −4𝑥 + 6
Graph the system: { 𝑦 < 3𝑥 − 1
𝑦 ≥ −2𝑥 − 3
3
12.)
Ann has decided to buy no more than 50 dining-room tables to sell at her furniture store.
She has also decided to restrict herself to buying only oak and mahogany tables. Ann wants to
buy at least 10 oak tables and at least 15 but no more than 25 mahogany tables.
A. Write a system of linear inequalities to represent the constraints Ann has set.
B. Ann earns a profit of $250 on each oak table that she sells and a profit of $175 on each mahogany
table that she sells. Write the objective function that Ann would use to maximize her profit from
the tables.
13.)
Find the maximum and minimum value of the objective function P = 345x + 125y on the
feasible area shown below.
14.)
Graph the parametric equations for the given interval of t.
𝑡
{
2 𝑓𝑜𝑟 − 4 ≤ 𝑡 ≤ 4
𝑦(𝑡) = 𝑡 − 1
𝑥(𝑡) =
4
Find a single equation in x and y that is equivalent to the parametric equations above.
15.)
The perimeter of a pasture is 1250 feet. The pasture is four times longer than it is wide.
Find the dimensions by setting up a system of equations and solving.
16.)
A chemist mixes some 20% acid solution with pure 100% acid to increase the
concentration of a solution. How much pure acid and acid solution should be mixed to form 100
milliliters of 40% acid solution?
17.)
A golf ball is hit off the ground with a nine-iron. The following parametric equations
describe the ball’s path:
{
𝑥(𝑡) = 30𝑡
𝑦(𝑡) = 120𝑡 − 16𝑡 2
The variables x and y are measured in feet per second, and t is measured in seconds. What
distance will the golf ball travel before it hits the ground?
5
18.)
A catcher throws the baseball from home plate to second base. The following parametric
equations describe the ball’s path:
{
𝑥(𝑡) = 80𝑡
𝑦(𝑡) = 15𝑡 − 16𝑡 2
The variables x and y are measured in feet per second, and t is measured in seconds. What
horizontal distance will the baseball travel before it hits the ground?
19.)
An investor wants to earn at least $1400 from investments. She plans to invest at most
$10,000 in two funds. One fund pays 13% interest and the other fund pays 15% interest, but has a
little more risk. Let x be the amount invested at 13% and let y be the amount invested at 15%.
Write and graph a system of inequalities to represent this situation. How much should be invest in
each fund?
20.)
A factory employs skilled laborers at $25 per hour and unskilled laborers at $12 per hour.
The hourly cost of the factory’s 24 workers is $405. How many of each type of laborer works at
the factory?
21.)
A vendor at the country fair wishes to invest $300 in his milkshake booth and would like
his total revenue to be $900. He figures he can make a small shake for $0.40 and a large shake for
$0.68. He plans to sell a small shake for $1.25 and a large shake for $2.00. How many of each
size shake will be need to make and sell to realize his revenue?
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22.)
A person invests in a mutual fund, part of which earned 11% interest and part of which
earned 6.5%. If the total amount invested was $5000 and the interest was $345, how much was
invested at each rate?
23.)
A chemist needs to create at 38% saline solution by using a 20% saline solution and a 50%
saline solution. If x is the amount of 20% solution and y is the amount of 50% solution, how much
of each solution must the chemist use to make 300 milliliters of a 38% solution?
24.)
Write a system of inequalities to represent the graph below. Find the values for the
vertices.
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