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Algebra A Combined Function

Elayn Martin-Gay

Chapter 4

Systems of Equations - all with Video Answers

Educators

Section 1

Solving Systems of Linear Equations by Graphing

01:56

Problem 1

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}x+y=8 \\ 3 x+2 y=21\end{array}\right.$
a. (2,4)
b. (5,3)

Catheryn Taylor
Catheryn Taylor
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02:09

Problem 2

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}2 x+y=5 \\ x+3 y=5\end{array}\right.$
a. (5,0)
b. (2,1)

Catheryn Taylor
Catheryn Taylor
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02:48

Problem 3

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}3 x-y=5 \\ x+2 y=11\end{array}\right.$
a. (3,4)
b. (0,-5)

Catheryn Taylor
Catheryn Taylor
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03:26

Problem 4

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}2 x-3 y=8 \\ x-2 y=6\end{array}\right.$
a. (-2,-4)
b. (7,2)

Catheryn Taylor
Catheryn Taylor
Numerade Educator
04:45

Problem 5

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}2 y=4 x+6 \\ 2 x-y=-3\end{array}\right.$
a. (-3,-3)
b. (0,3)

Catheryn Taylor
Catheryn Taylor
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04:19

Problem 6

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}x+5 y=-4 \\ -2 x=10 y+8\end{array}\right.$
a. (-4,0)
b. (6,-2)

Catheryn Taylor
Catheryn Taylor
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05:52

Problem 7

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}-2=x-7 y \\ 6 x-y=13\end{array}\right.$
a. (-2,0)
b. $\left(\frac{1}{2}, \frac{5}{14}\right)$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
04:37

Problem 8

Determine whether each ordered pair is a solution of the system of linear equations. See Examples 1 and $2 .$
$\left\{\begin{array}{l}4 x=1-y \\ x-3 y=-8\end{array}\right.$
a. (0,1)
b. $\left(\frac{1}{6}, \frac{1}{3}\right)$

Catheryn Taylor
Catheryn Taylor
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01:34

Problem 9

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+y=4 \\ x-y=2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:24

Problem 10

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+y=3 \\ x-y=5\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:29

Problem 11

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+y=6 \\ -x+y=-6\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
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01:33

Problem 12

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+y=1 \\ -x+y=-3\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:04

Problem 13

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=2 x \\ 3 x-y=-2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:53

Problem 14

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=-3 x \\ 2 x-y=-5\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:33

Problem 15

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=x+1 \\ y=2 x-1\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:40

Problem 16

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=3 x-4 \\ y=x+2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:59

Problem 17

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}2 x+y=0 \\ 3 x+y=1\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:52

Problem 18

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}2 x+y=1 \\ 3 x+y=0\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:41

Problem 19

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=-x-1 \\ y=2 x+5\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:58

Problem 20

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=x-1 \\ y=-3 x-5\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:09

Problem 21

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+y=5 \\ x+y=6\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
00:58

Problem 22

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x-y=4 \\ x-y=1\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:49

Problem 23

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}2 x-y=6 \\ y=2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:25

Problem 24

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+y=5 \\ x=4\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:56

Problem 25

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x-2 y=2 \\ 3 x+2 y=-2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:42

Problem 26

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x+3 y=7 \\ 2 x-3 y=-4\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
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01:08

Problem 27

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}2 x+y=4 \\ 6 x=-3 y+6\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
00:58

Problem 28

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y+2 x=3 \\ 4 x=2-2 y\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:28

Problem 29

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y-3 x=-2 \\ 6 x-2 y=4\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:25

Problem 30

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x-2 y=-6 \\ -2 x+4 y=12\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
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00:57

Problem 31

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x=3 \\ y=-1\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:08

Problem 32

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}x=-5 \\ y=3\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:39

Problem 33

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=x-2 \\ y=2 x+3\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:42

Problem 34

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}y=x+5 \\ y=-2 x-4\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:52

Problem 35

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}2 x-3 y=-2 \\ -3 x+5 y=5\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:32

Problem 36

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}4 x-y=7 \\ 2 x-3 y=-9\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:19

Problem 37

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}6 x-y=4 \\ \frac{1}{2} y=-2+3 x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:12

Problem 38

Solve each system of linear equations by graphing. See Examples 3 through $6 .$
$\left\{\begin{array}{l}3 x-y=6 \\ \frac{1}{3} y=-2+x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:39

Problem 39

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}4 x+y=24 \\ x+2 y=2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:08

Problem 40

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}3 x+y=1 \\ 3 x+2 y=6\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:35

Problem 41

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}2 x+y=0 \\ 2 y=6-4 x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:06

Problem 42

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}3 x+y=0 \\ 2 y=-6 x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
00:59

Problem 43

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}4 x-y=6 \\ \frac{1}{2} y=-3+2 x\end{array}\right.$

Erika Bustos
Erika Bustos
Numerade Educator
02:39

Problem 44

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}3 x-y=2 \\ \frac{1}{3} y=-2+3 x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:13

Problem 45

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}x=5 \\ y=-2\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:15

Problem 46

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}y=3 \\ x=-4\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:29

Problem 47

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}3 y-2 x=3 \\ x+2 y=9\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:25

Problem 48

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}2 y=x+2 \\ y+2 x=3\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:56

Problem 49

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}6 y+4 x=6 \\ 3 y-3=-2 x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
02:36

Problem 50

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}8 y+6 x=4 \\ 4 y-2=3 x\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:53

Problem 52

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}x+y=4 \\ x+y=3\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
01:51

Problem 52

Without graphing, decide.
a. Are the graphs of the equations identical lines, parallel lines, or lines intersecting at a single point?
b. How many solutions does the system have? See Examples 7 and 8 .
$\left\{\begin{array}{l}2 x+y=0 \\ y=-2 x+1\end{array}\right.$

Catheryn Taylor
Catheryn Taylor
Numerade Educator
00:19

Problem 53

Solve each equation. See Section $2.3 .$
$5(x-3)+3 x=1$

Erika Bustos
Erika Bustos
Numerade Educator
00:17

Problem 54

Solve each equation. See Section $2.3 .$
$-2 x+3(x+6)=17$

Erika Bustos
Erika Bustos
Numerade Educator
00:29

Problem 55

Solve each equation. See Section $2.3 .$
$4\left(\frac{y+1}{2}\right)+3 y=0$

Erika Bustos
Erika Bustos
Numerade Educator
00:26

Problem 56

Solve each equation. See Section $2.3 .$
$-y+12\left(\frac{y-1}{4}\right)=3$

Erika Bustos
Erika Bustos
Numerade Educator
00:17

Problem 57

Solve each equation. See Section $2.3 .$
$8 a-2(3 a-1)=6$

Erika Bustos
Erika Bustos
Numerade Educator
00:24

Problem 58

Solve each equation. See Section $2.3 .$
$3 z-(4 z-2)=9$

Erika Bustos
Erika Bustos
Numerade Educator
01:22

Problem 59

Draw a graph of two linear equations whose associated system has the solution (-1,4) .

Catheryn Taylor
Catheryn Taylor
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01:37

Problem 60

Draw a graph of two linear equations whose associated system has the solution (3,-2) .

Catheryn Taylor
Catheryn Taylor
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00:52

Problem 61

Draw a graph of two linear equations whose associated system has no solution.

Catheryn Taylor
Catheryn Taylor
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01:07

Problem 62

Draw a graph of two linear equations whose associated system has an infinite number of solutions.

Catheryn Taylor
Catheryn Taylor
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00:28

Problem 63

The double line graph below shows the number of pounds of fishery products from U.S. domestic catch and from imports. Use this graph to answer Exercises 63 and 64. (Source: Statistical Abstract of the United States).
Between what pairs of years did the number of pounds of imported fishery products equal the number of pounds of domestic catch?

Erika Bustos
Erika Bustos
Numerade Educator
00:24

Problem 64

The double line graph below shows the number of pounds of fishery products from U.S. domestic catch and from imports. Use this graph to answer Exercises 63 and 64. (Source: Statistical Abstract of the United States).
For what year(s) was the number of pounds of imported fishery products less than the number of pounds of domestic catch?

Erika Bustos
Erika Bustos
Numerade Educator
00:27

Problem 65

The double line graph below shows the average attendance per game for the years shown for the Minnesota Twins and the Texas Rangers baseball teams. Use this for Exercises 65 and 66. (Source: Baseball Almanac).
In what year(s) was the average attendance per game for the Texas Rangers greater than the average attendance per game for the Minnesota Twins?

Erika Bustos
Erika Bustos
Numerade Educator
00:43

Problem 66

The double line graph below shows the average attendance per game for the years shown for the Minnesota Twins and the Texas Rangers baseball teams. Use this for Exercises 65 and 66. (Source: Baseball Almanac).
In what year was the average attendance per game for the Texas Rangers closest to the average attendance per game for the Minnesota Twins, 2003 or $2006 ?$

Erika Bustos
Erika Bustos
Numerade Educator
00:44

Problem 67

Construct a system of two linear equations that has (2,5) as a solution.

Erika Bustos
Erika Bustos
Numerade Educator
00:35

Problem 68

Construct a system of two linear equations that has (0,1) as a solution.

Erika Bustos
Erika Bustos
Numerade Educator
01:33

Problem 69

The ordered pair (-2,3) is a solution of the three linear equations below:
$x+y=1$
$2 x-y=-7$
$x+3 y=7$
If each equation has a distinct graph, describe the graph of all three equations on the same axes.

Erika Bustos
Erika Bustos
Numerade Educator
01:42

Problem 70

Explain how to use a graph to determine the number of solutions of a system.

Catheryn Taylor
Catheryn Taylor
Numerade Educator
00:58

Problem 71

Below are tables of values for two linear equations.
a. Find a solution of the corresponding system.
b. Graph several ordered pairs from each table and sketch the two lines.
C. Does your graph confirm the solution from part (a)?

Erika Bustos
Erika Bustos
Numerade Educator
00:51

Problem 72

Below are tables of values for two linear equations.
a. Find a solution of the corresponding system.
b. Graph several ordered pairs from each table and sketch the two lines.
C. Does your graph confirm the solution from $\operatorname{part}(\mathrm{a}) ?$

Erika Bustos
Erika Bustos
Numerade Educator