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Algebra 2

Holliday, Luchin, Cuevas, Carter Marks, Day, Casey, Hayek

Chapter 3

Systems of Equations and Inequalities - all with Video Answers

Educators


Section 1

Solving Systems of Equations by Graphing

02:52

Problem 1

Solve each system of equations by completing a table.
$y=2 x+9$
$y=-x+3$

Alanya Huang
Alanya Huang
Numerade Educator
04:42

Problem 2

Solve each system of equations by completing a table.
$3 x+2 y=10$
$2 x+3 y=10$

Alanya Huang
Alanya Huang
Numerade Educator
03:57

Problem 3

Solve each system of equations by graphing.
$4 x-2 y=22$
$6 x+9 y=-3$

Alanya Huang
Alanya Huang
Numerade Educator
00:52

Problem 4

Solve each system of equations by graphing.
$y=2 x-4$
$y=-3 x+1$

Alanya Huang
Alanya Huang
Numerade Educator
02:31

Problem 5

Developing Digital Photos
EZ Online Digital Photos Charges
$\$ 0.15$ per digital photo and
$\$ 2.70$ for shipping
Local Pharmacy Charges $\$ 0.25$ per digital photo

Write equations that represent the cost of printing digital photos at each lab.

Alanya Huang
Alanya Huang
Numerade Educator
03:15

Problem 6

Developing Digital Photos
EZ Online Digital Photos Charges
$\$ 0.15$ per digital photo and
$\$ 2.70$ for shipping
Local Pharmacy Charges $\$ 0.25$ per digital photo

Under what conditions is the cost to print digital photos the same for either store?

Alanya Huang
Alanya Huang
Numerade Educator
01:36

Problem 7

Developing Digital Photos
EZ Online Digital Photos Charges
$\$ 0.15$ per digital photo and
$\$ 2.70$ for shipping
Local Pharmacy Charges $\$ 0.25$ per digital photo

When is it best to use EZ Online Digital Photos and when is it best to use the local pharmacy?

Alanya Huang
Alanya Huang
Numerade Educator
01:46

Problem 8

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$y=6-x$
$y=x+4$

Alanya Huang
Alanya Huang
Numerade Educator
24:17

Problem 9

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$x+2 y=2$
$2 x+4 y=8$

Alanya Huang
Alanya Huang
Numerade Educator
04:01

Problem 10

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$x-2 y=8$
$\frac{1}{2} x-y=4$

Alanya Huang
Alanya Huang
Numerade Educator
03:10

Problem 11

Solve each system of linear equations by completing a table.
$y=3 x-8$
$y=x-8$

Alanya Huang
Alanya Huang
Numerade Educator
04:07

Problem 12

Solve each system of linear equations by completing a table.
$x+2 y=6$
$2 x+y=9$

Alanya Huang
Alanya Huang
Numerade Educator
03:06

Problem 13

Solve each system of linear equations by graphing.
$2 x+3 y=12$
$2 x-y=4$

Alanya Huang
Alanya Huang
Numerade Educator
03:48

Problem 14

Solve each system of linear equations by graphing.
$3 x-7 y=-6$
$x+2 y=11$

Alanya Huang
Alanya Huang
Numerade Educator
02:52

Problem 15

Solve each system of linear equations by graphing.
$5 x-11=4 y$
$7 x-1=8 y$

Alanya Huang
Alanya Huang
Numerade Educator
03:00

Problem 16

Solve each system of linear equations by graphing.
$2 x+3 y=7$
$2 x-3 y=7$

Alanya Huang
Alanya Huang
Numerade Educator
03:12

Problem 17

Solve each system of linear equations by graphing.
$8 x-3 y=-3$
$4 x-2 y=-4$

Alanya Huang
Alanya Huang
Numerade Educator
03:28

Problem 18

Solve each system of linear equations by graphing.
$\frac{1}{4} x+2 y=5$
$2 x-y=6$

Alanya Huang
Alanya Huang
Numerade Educator
01:27

Problem 19

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$y=x+4$
$y=x-4$

Alanya Huang
Alanya Huang
Numerade Educator
01:51

Problem 20

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$y=x+3$
$y=2 x+6$

Alanya Huang
Alanya Huang
Numerade Educator
03:08

Problem 21

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$x+y=4$
$-4 x+y=9$

Alanya Huang
Alanya Huang
Numerade Educator
02:59

Problem 22

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$3 x+y=3$
$6 x+2 y=6$

Alanya Huang
Alanya Huang
Numerade Educator
03:08

Problem 23

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$y-x=5$
$2 y-2 x=8$

Alanya Huang
Alanya Huang
Numerade Educator
03:31

Problem 24

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$4 x-2 y=6$
$6 x-3 y=9$

Alanya Huang
Alanya Huang
Numerade Educator
03:21

Problem 25

The sides of an angle are parts of two lines whose equations are $2 y+3 x=-7$ and $3 y-2 x=9$ . The angle's vertex is the point where the two sides meet. Find the coordinates of the vertex of the angle.

Alanya Huang
Alanya Huang
Numerade Educator
04:26

Problem 26

The graphs of $y-2 x=1,4 x+y=7,$ and $2 y-x=-4$ contain the sides of a triangle. Find the coordinates of the vertices of the triangle.

Alanya Huang
Alanya Huang
Numerade Educator
02:25

Problem 27

In economics, the point at which the supply equals the demand is the equilibrium price. If the supply of a product is greater than the demand, there is a surplus and prices fall. If the supply is less than the demand, there is a shortage and prices rise.
If the price for vitamins is $\$ 8.00$ a bottle, what is the supply of the product and what is the demand? Will prices tend to rise or fall?

Alanya Huang
Alanya Huang
Numerade Educator
02:28

Problem 28

In economics, the point at which the supply equals the demand is the equilibrium price. If the supply of a product is greater than the demand, there is a surplus and prices fall. If the supply is less than the demand, there is a shortage and prices rise.
If the price for vitamins is $\$ 12.00$ a bottle, what is the supply of the product and what is the demand? Will prices tend to rise or fall?

Alanya Huang
Alanya Huang
Numerade Educator
01:31

Problem 29

In economics, the point at which the supply equals the demand is the equilibrium price. If the supply of a product is greater than the demand, there is a surplus and prices fall. If the supply is less than the demand, there is a shortage and prices rise.
At what quantity will the prices stabilize? What is the equilibrium price for this product?

Alanya Huang
Alanya Huang
Numerade Educator
03:04

Problem 30

Use the table showing state populations.
$\begin{array}{|c|c|c|c|c|}\hline 1 & {\text { California }} & {25,484,000} & {567,000} \\ \hline 2 & {\text { Texas }} & {22,118,000} & {447,000} \\ \hline 3 & {\text { New York }} & {19,190,000} & {70,000} \\ \hline 4 & {\text { Florida }} & {17,019,000} & {304,000} \\ \hline 5 & {\text { lllinois }} & {12,653,000} & {80,000} \\ \hline\end{array}$
Write equations that represent the populations of Florida and New York $x$ years after 2003. Assume that both states continue to gain the same number of residents every year. Let $y$ equal the population.

Alanya Huang
Alanya Huang
Numerade Educator
02:34

Problem 31

Use the table showing state populations.
$\begin{array}{|c|c|c|c|c|}\hline 1 & {\text { California }} & {25,484,000} & {567,000} \\ \hline 2 & {\text { Texas }} & {22,118,000} & {447,000} \\ \hline 3 & {\text { New York }} & {19,190,000} & {70,000} \\ \hline 4 & {\text { Florida }} & {17,019,000} & {304,000} \\ \hline 5 & {\text { lllinois }} & {12,653,000} & {80,000} \\ \hline\end{array}$
Graph both equations for the years 2003 to 2020. Estimate when the populations of both states will be equal.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
02:46

Problem 32

Use the table showing state populations.
$\begin{array}{|c|c|c|c|c|}\hline 1 & {\text { California }} & {25,484,000} & {567,000} \\ \hline 2 & {\text { Texas }} & {22,118,000} & {447,000} \\ \hline 3 & {\text { New York }} & {19,190,000} & {70,000} \\ \hline 4 & {\text { Florida }} & {17,019,000} & {304,000} \\ \hline 5 & {\text { lllinois }} & {12,653,000} & {80,000} \\ \hline\end{array}$
Do you think New York will overtake Texas as the second most populous state by 2010? by 2020? Explain your reasoning.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
02:50

Problem 33

Solve each system of equations by graphing.
$\frac{2}{3} x+y=-3$
$y-\frac{1}{3} x=6$

Alanya Huang
Alanya Huang
Numerade Educator
04:37

Problem 34

Solve each system of equations by graphing.
$\frac{1}{2} x-y=0$
$\frac{1}{4} x+\frac{1}{2} y=-2$

Alanya Huang
Alanya Huang
Numerade Educator
05:46

Problem 35

Solve each system of equations by graphing.
$\frac{4}{3} x+\frac{1}{5} y=3$
$\frac{2}{3} x-\frac{3}{5} y=5$

Alanya Huang
Alanya Huang
Numerade Educator
03:32

Problem 36

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$1.6 y=0.4 x+1$
$0.4 y=0.1 x+0.25$

Alanya Huang
Alanya Huang
Numerade Educator
02:56

Problem 37

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$3 y-x=-2$
$y-\frac{1}{3} x=2$

Alanya Huang
Alanya Huang
Numerade Educator
04:04

Problem 38

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
$2 y-4 x=3$
$\frac{4}{3} x-y=-2$

Alanya Huang
Alanya Huang
Numerade Educator
00:35

Problem 39

To use a TI-83/84 Plus to solve a system of equations, graph the equations. Then, select INTERSECT, which is option 5 under the CALC menu, to find the coordinates of the point of intersection to the nearest hundredth.
$y=0.125 x-3.005$
$y=-2.58$

Alanya Huang
Alanya Huang
Numerade Educator
00:58

Problem 40

To use a TI-83/84 Plus to solve a system of equations, graph the equations. Then, select INTERSECT, which is option 5 under the CALC menu, to find the coordinates of the point of intersection to the nearest hundredth.
$3.6 x-2 y=4$
$-2.7 x+y=3$

Alanya Huang
Alanya Huang
Numerade Educator
00:30

Problem 41

To use a TI-83/84 Plus to solve a system of equations, graph the equations. Then, select INTERSECT, which is option 5 under the CALC menu, to find the coordinates of the point of intersection to the nearest hundredth.
$y=0.18 x+2.7$
$y=-0.42 x+5.1$

Alanya Huang
Alanya Huang
Numerade Educator
01:18

Problem 42

Give an example of a system of equations that is consistent and independent.

Alanya Huang
Alanya Huang
Numerade Educator
01:39

Problem 43

Explain why a system of linear equations cannot have exactly two solutions.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
04:40

Problem 44

State the conditions for which the system below is:
(a) consistent and dependent, (b) consistent and independent, and
(c) inconsistent if none of the variables are equal to 0.
$a x+b y=c$
$d x+e y=f$

Kirsten Bauck
Kirsten Bauck
Numerade Educator
02:39

Problem 45

Use the information about sales on page 116 to explain how a system of equations can be used to predict sales. Include an explanation of the meaning of the solution of the system of equations in the application at the beginning of the lesson. How reasonable would it be to use this system of equations to predict the company’s online and in-store profits in 100 years? Explain your reasoning.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
03:42

Problem 46

Which of the following best describes the graph of the equations?
$4 y=3 x+8$
$-6 x=-8 y+24$
A. The lines are parallel.
B. The lines have the same $x$-intercept.
C. The lines are perpendicular.
D. The lines have the same $y$-intercept.

Alanya Huang
Alanya Huang
Numerade Educator
03:12

Problem 47

Which set of dimensions corresponds to a triangle similar to the one shown below?
F. 7 units, 11 units, 12 units
G. 10 units, 23 units, 24 units
H. 20 units, 48 units, 52 units
J. 1 unit, 2 units, 3 units

Kirsten Bauck
Kirsten Bauck
Numerade Educator
01:41

Problem 48

Simon is putting up fence around his yard at a rate no faster than 15 feet per hour. Draw a graph that represents the length of fence that Simon has built.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
02:18

Problem 49

Identify each function as S for step, C for constant, A for absolute value, or P for piecewise.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
01:17

Problem 50

Identify each function as S for step, C for constant, A for absolute value, or P for piecewise.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
01:27

Problem 51

Identify each function as S for step, C for constant, A for absolute value, or P for piecewise.

Kirsten Bauck
Kirsten Bauck
Numerade Educator
01:34

Problem 52

Simplify each expression.
$(3 x+5)-(2 x+3)$

Alanya Huang
Alanya Huang
Numerade Educator
01:16

Problem 53

Simplify each expression.
$(3 y-11)+(6 y+12)$

Alanya Huang
Alanya Huang
Numerade Educator
01:20

Problem 54

Simplify each expression.
$(5 x-y)+(-8 x+7 y)$

Alanya Huang
Alanya Huang
Numerade Educator
00:59

Problem 55

Simplify each expression.
6$(2 x+3 y-1)$

Alanya Huang
Alanya Huang
Numerade Educator
01:46

Problem 56

Simplify each expression.
5$(4 x+2 y-x+2)$

Alanya Huang
Alanya Huang
Numerade Educator
01:50

Problem 57

Simplify each expression.
$3(x+4 y)-2(x+4 y)$

Alanya Huang
Alanya Huang
Numerade Educator