Mid-Chapter Quiz: Lessons 6-1 through 6-4 Use the graph to determine whether each system is consistent or inconsistent and if it is independent or dependent.
SOLUTION: The lines y = −2x + 3 and y = −2x − 3 never intersect which means this system has no solution. So, the system is inconsistent. Graph each system and determine the number of solutions that it has. If it has one solution, name it. 4. x + y = 6 x −y = 4 SOLUTION: To graph the system, write both equations in slopeintercept form. y = –x + 6 y=x–4
2. y = −2x + 3 y = −2x − 3 SOLUTION: The lines y = −2x + 3 and y = −2x − 3 never intersect which means this system has no solution. So, the system is inconsistent. Graph each system and determine the number of solutions that it has. If it has one solution, name it. 4. x + y = 6 x −y = 4 SOLUTION: To graph the system, write both equations in slopeintercept form. y = –x + 6 y=x–4
The graphs appear to intersect at the point (5, 1). You can check this by substituting 5 for x and 1 for y.
The solution is (5, 1). 6. x − 4y = −6 y = −1 SOLUTION: To graph the system, write both equations in slopeintercept form. The graphs appear to intersect at the point (5, 1). You can check this by substituting 5 for x and 1 for y.
Graph eSolutions Manual - Powered by Cognero
The solution is (5, 1).
and y = –1. Page 1
Mid-Chapter Quiz: 6-1 through 6-4 The solution is (5,Lessons 1). 6. x − 4y = −6 y = −1
The solution is (–10, –1). 8. 2x + y = −4 5x + 3y = −6
SOLUTION: To graph the system, write both equations in slopeintercept form.
SOLUTION: To graph the system, write both equations in slopeintercept form. Equation 1:
Equation 2:
Graph
and y = –1. Graph y = –2x − 4 and
The graphs appear to intersect at the point (–10, –1). You can check this by substituting –10 for x and –1 for y.
The solution is (–10, –1).
.
The graphs appear to intersect at the point (–6, 8). You can check this by substituting –6 for x and 8 for y.
8. 2x + y = −4 5x + 3y = −6 SOLUTION: To graph the system, write both equations in slopeintercept form. Equation 1:
Equation 2: eSolutions Manual - Powered by Cognero
The solution is (–6, 8). Use substitution to solve each system of equations. 10. y = −2x − 3 x +y = 9 SOLUTION: y = −2x − 3 x +y = 9
Page 2
Mid-Chapter Quiz: Lessons 6-1 through 6-4 The solution is (–6, 8). Use substitution to solve each system of equations. 10. y = −2x − 3 x +y = 9 SOLUTION: y = −2x − 3 x +y = 9 Substitute −2x − 3 for y in the second equation.
The solution is (–12, 21). 12. y = −4x 6x − y = 30 SOLUTION: y = −4x 6x − y = 30 Substitute −4x for y in the second equation.
Use the solution for x and either equation to find the value for y.
Use the solution for x and either equation to find the value for y.
The solution is (3, –12). 14. AMUSEMENT PARKS The cost of two groups going to an amusement park is shown in the table. The solution is (–12, 21).
12. y = −4x 6x − y = 30 SOLUTION: y = −4x 6x − y = 30 Substitute −4x for y in the second equation.
a. Define variables to represent the cost of an adult ticket and the cost of a child ticket.
b. Write a system of equations to find the cost of an adult and child admission.
c. Solve the system of equations, and explain what the solution means.
Use the solution for x and either equation to find the value for y.
d. How much will a group of 3 adults and 5 children be charged for admission? SOLUTION: a. Let a = cost of an adult ticket and c = the cost of a child ticket.
The solution is (3, –12).
eSolutions Manual - Powered by Cognero
14. AMUSEMENT PARKS The cost of two groups going to an amusement park is shown in the table.
b. The cost of a group with 4 adults and 2 children is $184. So, 4a + 2c = 184. The cost of a group with 4 adults and 3 children is $200. So, 4a + 3c = 200. Page 3
a. Let a = cost of an adult ticket and c = the cost of a child ticket.
Mid-Chapter Quiz: Lessons 6-1 through 6-4 b. The cost of a group with 4 adults and 2 children is $184. So, 4a + 2c = 184. The cost of a group with 4 adults and 3 children is $200. So, 4a + 3c = 200.
Notice that the coefficients of the a terms are the same, so subtract the equations.
Use the solution for c in either equation to find the value of a.
The cost of an adult’s ticket is $38, and the cost of a child’s ticket is $16.
the total cost of admission. A group of 3 adults and 5 children visiting the amusement park will be charged $194 for admission. Use elimination to solve each system of equations. 16. x + y = 9 x − y = −3 SOLUTION: Because y and −y have opposite coefficients, add the equations.
Now, substitute 3 for x in either equation to find the value of y.
The solution is (3, 6).
d. Substitute these values into the equation to find the total cost of admission. A group of 3 adults and 5 children visiting the amusement park will be charged $194 for admission. Use elimination to solve each system of equations. 16. x + y = 9 x − y = −3
18. 9x − 24y = −6 3x + 4y = 10 SOLUTION: Multiply each term in the second equation by −3 to eliminate the x coefficient.
Because 9x and −9x have opposite coefficients, add the equations.
SOLUTION: Because y and −y have opposite coefficients, add the equations.
Now, substitute 1 for y in either equation to find the value of y. Now, substitute 3 for x in either equation to find the value of y.
The solution is (3, 6). eSolutions Manual - Powered by Cognero
18. 9x − 24y = −6 3x + 4y = 10
The solution is (2, 1). Page 4 20. MULTIPLE CHOICE The Blue Mountain High School Drama Club is selling tickets to their spring musical. Adult tickets are $4 and student tickets are
Mid-Chapter Quiz: Lessons 6-1 through 6-4 The solution is (2, 1). 20. MULTIPLE CHOICE The Blue Mountain High School Drama Club is selling tickets to their spring musical. Adult tickets are $4 and student tickets are $1. A total of 285 tickets are sold for $765. How many of each type of ticket are sold?
F 145 adult, 140 student
G 120 adult, 165 student
H 180 adult, 105 student
J 160 adult, 125 student SOLUTION: Let a = the number of adult tickets sold and s = the number of student tickets sold. So, a + s = 285 and 4a + 1s = 765. Solve the first equation for s.
Substitute 285 – a for s in the second equation.
Use the solution for a in either equation to find the value of s.
160 adult tickets and 125 student tickets were sold. So, J is the correct choice.
eSolutions Manual - Powered by Cognero
Page 5
