Algebra 1: Concepts and Skills

Ron Larson, Laurie Boswell, Holt McDougal

Chapter 7 System of Linear Equations and Inequalities - all with Video Answers

Educators

Section 1

Graphing Linear Systems

01:13

Problem 1

Explain what it means to solve a linear system using the graph-and-check method.

Jordan C

Numerade Educator

00:27

Problem 2

Use the graph at the right to find the point of intersection for the system of linear equations.
$$
\begin{array}{l}
{y=-x+2} \\
{y=x+2}
\end{array}
$$

Jordan C

Numerade Educator

00:43

Problem 3

Use the linear system below.
$$
\begin{array}{l}
{-x+y=-2} \\
{2 x+y=10}
\end{array}
$$
Write each equation in slope-intercept form.

Jordan C

Numerade Educator

01:21

Problem 4

Use the linear system below.
$$
\begin{array}{l}
{-x+y=-2} \\
{2 x+y=10}
\end{array}
$$
Graph both equations in the same coordinate plane.

Jordan C

Numerade Educator

00:21

Problem 5

Use the linear system below.
$$
\begin{array}{l}
{-x+y=-2} \\
{2 x+y=10}
\end{array}
$$
Estimate the coordinates of the point of intersection.

Jordan C

Numerade Educator

01:10

Problem 6

Use the linear system below.
$$
\begin{array}{l}
{-x+y=-2} \\
{2 x+y=10}
\end{array}
$$
Check the coordinates algebraically by substituting them into each equation of the original linear system.

Daniel Mcconnell

Numerade Educator

01:31

Problem 7

Check whether the ordered pair is a solution of the system of linear equations.
$$
\begin{array}{l}
{3 x-2 y=11} \\
{-x+6 y=7}
\end{array}
$$
$$
(5,2)
$$

Daniel Mcconnell

Numerade Educator

01:32

Problem 8

Check whether the ordered pair is a solution of the system of linear equations.
$$
\begin{array}{c}
{6 x-3 y=-15} \\
{2 x+y=-3}
\end{array} \quad(-2,1)
$$

Daniel Mcconnell

Numerade Educator

01:15

Problem 9

Check whether the ordered pair is a solution of the system of linear equations.
$$
\begin{array}{c}
{x+3 y=15} \\
{4 x+y=6}
\end{array} \quad(3,-6)
$$

Daniel Mcconnell

Numerade Educator

01:40

Problem 10

Check whether the ordered pair is a solution of the system of linear equations.
$$
\begin{array}{c}
{-5x+y=19} \\
{ x-7y=3}
\end{array} \quad(-4,-1)
$$

Daniel Mcconnell

Numerade Educator

01:12

Problem 11

Check whether the ordered pair is a solution of the system of linear equations.
$$
\begin{array}{c}
{-15x+7y=1} \\
{ 3x-y=1}
\end{array} \quad(3,5)
$$

Daniel Mcconnell

Numerade Educator

01:10

Problem 12

Check whether the ordered pair is a solution of the system of linear equations.
$$
\begin{array}{c}
{-2x+y=11} \\
{ -x-9y=-15}
\end{array} \quad(6,1)
$$

Daniel Mcconnell

Numerade Educator

01:17

Problem 13

Use the graph given to estimate the solution of the linear system. Then check your solution algebraically.
$$
\begin{array}{r}
{-x+2 y=6} \\
{x+4 y=24}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

01:43

Problem 14

Use the graph given to estimate the solution of the linear system. Then check your solution algebraically.
$$
\begin{aligned}
&2 x-y=-2\\
&4 x-y=-6
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

01:22

Problem 15

Use the graph given to estimate the solution of the linear system. Then check your solution algebraically.
$$
\begin{aligned}
x+y &=3 \\
-2 x+y &=-6
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

02:12

Problem 16

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{aligned}
&y=-x+3\\
&y=x+1
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

02:02

Problem 17

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{aligned}
&y=-6\\
&x=6
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

02:23

Problem 18

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{array}{c}
{y=2 x-4} \\
{2 y=-x}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

02:05

Problem 19

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{array}{r}
{2 x-3 y=9} \\
{x=-3}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

02:16

Problem 20

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{aligned}
5 x+4 y &=16 \\
y &=-16
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

02:04

Problem 21

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{array}{r}
{x-y=1} \\
{5 x-4 y=0}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

02:10

Problem 22

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{array}{r}
{3 x+6 y=15} \\
{-2 x+3 y=-3}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

01:14

Problem 23

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{aligned}
&y=-2 x+6\\
&y=2 x+2
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

02:01

Problem 24

Estimate the solution of the linear system graphically. Then check the solution algebraically.
$$
\begin{array}{c}
{5 x+6 y=54} \\
{-x+y=9}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

02:18

CARS Car model A costs $\$ 22,000$ to purchase and $\$ .12$ per mile to maintain. Car model B costs $\$ 24,500$ to purchase and $\$ .10$ per mile to maintain.
Use the graph to determine how many miles each car must be driven for the total costs of the two models to be the same.

Daniel Mcconnell

Numerade Educator

03:03

Problem 26

AEROBICS CLASSES A fitness club offers an aerobics class in the morning and in the evening. Assuming that the number of people in each class can be represented by a linear function, use the information in the table below to predict when the number of people in each class will be the same.
$$
\begin{array}{|c|c|c|}
\hline \text { Class } & {\text { Current }} & {\text { Increase (people }} \\
\text { } & {\text { attendance }} & {\text { per month) }} \\
\hline \text { Morning } & {40} & {2} \\
\hline \text { Evening } & {22} & {8} \\
\hline
\end{array}
$$

Daniel Mcconnell

Numerade Educator

03:12

Problem 27

The fast-changing world of the 1920 s produced new roles for women in the workplace. From 1910 to 1930 the percent of women working in agriculture decreased, while the percent of women in professional jobs increased, as shown in the table.
$$
\begin{array}{|c|c|c|}
\hline \text { Job type } & {\text { Percent holding that }} & {\text { Average percent increase }} \\
& {\text { job type in } 1910} & {\text { per year from } 1910 \text { to } 1930} \\
\hline \text { Agriculture } & {22.4 \%} & {-0.7 \%} \\
\hline \text { Professional } & {9.1 \%} & {0.25 \%} \\
\hline
\end{array}
$$
Assuming that both percentages can be represented by a linear function, use the information in the table above to estimate when the percent of women working in agriculture equaled the percent of women working in professional jobs between 1910 and 1930

Daniel Mcconnell

Numerade Educator

02:05

Problem 28

You and your sister are saving money from your allowances. You have $\$ 25$ and save $\$ 3$ each week. Your sister has $\$ 40$ and saves $\$ 2$ each week. After how many weeks will you and your sister have the same amount of money?

Daniel Mcconnell

Numerade Educator

02:46

Problem 29

You know how to solve the equation $x+2=3 x-4$ algebraically. This equation can also be solved by graphing the following system of linear equations.
$$
\begin{aligned}
&y=x+2\\
&y=3 x-4
\end{aligned}
$$
a. Explain how the system of linear equations is related to the original equation given.
b. Estimate the solution of the linear system graphically.
c. Check that the $x$ -coordinate from part (b) satisfies the original equation by substituting the $x$ -coordinate for $x$ in $x+2=3 x-4$

Daniel Mcconnell

Numerade Educator

01:37

Problem 30

Which ordered pair is a solution of the following system of linear equations?
$$
\begin{array}{r}
{x+y=3} \\
{2 x+y=6}
\end{array}
$$
$$
\begin{array}{}{ \text A {(0,3)}}\quad { \text B {(1,2)}}\quad \quad { \text C {(2,1)}}\quad \quad { \text D {(3,0)}}
\end{array}
$$

Daniel Mcconnell

Numerade Educator

02:16

Problem 31

Which system of linear equations is graphed?
$$
F. \quad\begin{array}{l}
{-x+2 y=2} \\
{-3 x+4 y=2}
\end{array}
$$
$$
G. \quad\begin{aligned}
&x+2 y=2\\
&x-2 y=0
\end{aligned}
$$
$$
H. \quad\begin{array}{c}
{-2 x+y=1} \\
{-4 x+3 y=2}
\end{array}
$$
$$
J. \quad\begin{aligned}
&2 x+y=1\\
&4 x+3 y=2
\end{aligned}
$$

Daniel Mcconnell

Numerade Educator

00:48

Problem 32

Solve the equation.
$$
3 x+7=-2
$$

Daniel Mcconnell

Numerade Educator

01:04

Problem 33

Solve the equation.
$$
15-2 a=7
$$

Daniel Mcconnell

Numerade Educator

00:49

Problem 34

Solve the equation.
$$
2 y+3 y=5
$$

Daniel Mcconnell

Numerade Educator

01:17

Problem 35

Solve the equation.
$$
21=7(w-2)
$$

Daniel Mcconnell

Numerade Educator

01:29

Problem 36

Solve the equation.
$$
-2(t-5)=26
$$

Dharmendra Jain

Numerade Educator

01:36

Problem 37

Solve the equation.
$$
4(2 x+3)=-4
$$

Daniel Mcconnell

Numerade Educator

01:44

Problem 38

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
$$
(3,0), m=-4
$$

Daniel Mcconnell

Numerade Educator

01:21

Problem 39

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
$$
(-4,3), m=1
$$

Daniel Mcconnell

Numerade Educator

01:34

Problem 40

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
$$
(1,-5), m=4
$$

Daniel Mcconnell

Numerade Educator

01:48

Problem 41

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
$$
(-4,-1), m=-2
$$

Daniel Mcconnell

Numerade Educator

01:26

Problem 42

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
$$
(2,3), m=2
$$

Daniel Mcconnell

Numerade Educator

02:02

Problem 43

Write in slope-intercept form the equation of the line that passes through the given point and has the given slope.
$$
(-1,5), m=-3
$$

Daniel Mcconnell

Numerade Educator

01:21

Problem 44

The Verrazano-Narrows Bridge in New York is the longest suspension bridge in North America, with a main span of 4260 feet. Let $x$ represent the length (in feet) of every other suspension bridge in North America. Write an inequality that describes $x .$ Then graph the inequality.