Download 6-1 Skills Practice

6-1 Skills Practice
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Graphing Systems of Equations
Homework A: #1-8
Homework B: #1-6
Homework C: #1-4
Use the graph at the right to determine whether
each system is consistent or inconsistent and if it is
independent or dependent.
1. y = x – 1
y = –x + 1
2. x – y = –4
y=x+4
Graph each system and determine the number of solutions that it has. If it has one solution, name it.
3. 2x – y = 1
4. 3x + y = –3
5. y = x + 2
6. y – x = –1
7. x – y = 3
8. y = 2x + 3
y = –3
x – y = –2
x – 2y = 3
Unit 3 Homework Packet
3x + y = 3
x+y=3
3y = 6x – 6
6-2 Skills Practice
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Substitution
Homework A: #1-10
Homework B: #4-10
Homework C: #7-10
Use substitution to solve each system of equations.
1. y = 4x
x+y=5
2. y = 2x
x + 3y = –14
3. y = x – 1
x+y=3
4. x = y – 7
x + 8y = 2
5. 2x – 3y = 21
y=3–x
6. y = 5x – 8
4x + 3y = 33
7. 3x – y = 4
2x – 3y = –9
8. x + 4y = 8
2x – 5y = 29
9. 2x + 5y = 38
x – 3y = –3
10. x – 4y = 27
3x + y = –23
Unit 3 Homework Packet
6-3 Skills Practice
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Elimination Using Addition and Subtraction
Homework A: #1-8
Homework B: #3-8
Homework C: #5-8
Use elimination to solve each system of equations.
1. 3x + 4y = 19
3x + 6y = 33
2. x + 4y = –8
x – 4y = –8
3. 2x – 3y = 9
–5x – 3y = 30
4. x – y = 4
2x + y = –4
5. 6x – 2y = 32
4x – 2y = 18
6. 3x + 2y = –19
–3x – 5y = 25
7. Find the two numbers whose sum is 29 and whose difference is 15.
8. Two times a number added to another number is 25. Three times the first number minus the other number is 20. Find
the numbers.
Unit 3 Homework Packet
6-4 Skills Practice
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Elimination Using Multiplication
Homework A: #1-8
Homework B: #3-8
Homework C: #5-8
Use elimination to solve each system of equations.
1. 2x + 5y = 3
2. 2x + y = 3
3. 5x + 3y = –10
4. 2x + 3y = 14
5. 2x – 3y = 21
6. 3x + 2y = –26
–x + 3y = –7
3x + 5y = –6
5x – 2y = 25
–4x – 4y = –8
3x – 4y = 4
4x – 5y = –4
7. Two times a number plus three times another number equals 13. The sum of the two numbers is 7. What are the
numbers?
8. FUNDRAISING Trisha and Byron are washing and vacuuming cars to raise money for a class trip. Trisha raised $38
washing 5 cars and vacuuming 4 cars. Byron raised $28 by washing 4 cars and vacuuming 2 cars. Find the amount
they charged to wash a car and vacuum a car.
Unit 3 Homework Packet
6-5 Skills Practice
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Applying Systems of Linear Equations
Homework A: #1-8
Homework B: #3-8
Homework C: #5-8
Determine the best method to solve each system of equations. Then solve the system.
1. 5x + 3y = 16
2. 3x – 5y = 7
3. y = 3x – 24
4. –11x – 10y = 17
5. 4x + y = 24
6. 6x – y = –145
3x – 5y = –4
5x – y = 8
5x – y = 12
2x + 5y = 13
5x – 7y = 50
x = 4 – 2y
7. VEGETABLE STAND A roadside vegetable stand sells pumpkins for $5 each and squashes for $3 each. One day they
sold 6 more squash than pumpkins, and their sales totaled $98. Write and solve a system of equations to find how many
pumpkins and quash they sold?
8. INCOME Ramiro earns $20 per hour during the week and $30 per hour for overtime on the weekends. One week
Ramiro earned a total of $650. He worked 5 times as many hours during the week as he did on the weekend. Write
and solve a system of equations to determine how many hours of overtime Ramiro worked on the weekend.
Unit 3 Homework Packet
6-6 Skills Practice
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
Systems of Inequalities
Homework A: #1-8
Homework B: #3-8
Homework C: #5-8
Solve each system of inequalities by graphing.
1. x > –1
y ≤ –3
2. y > x + 3
y ≤ –1
3. x < 2
y–x≤2
4. y – x > 4
x+y>2
5. y > x + 1
y ≥ –x + 1
Write a system of inequalities for each graph.
7.
Unit 3 Homework Packet
6. y < 2x + 4
y≥x+1
8.