6 Mid-Chapter Quiz

Do you know HOW?

Solve each system by graphing. Tell whether the system has one solution, infinitely many solutions, or no solution.

1. y = x − 1 y = − 3 x − 5 table with 2 rows and 1 column , row1 column 1 , y equals x minus 1 , row2 column 1 , y equals negative 3 x minus 5 , end table
2. y = 4 3 x − 2 3 y − 4 x = − 6 table with 2 rows and 1 column , row1 column 1 , y equals , 4 thirds , x minus 2 , row2 column 1 , 3 y minus 4 x equals negative 6 , end table
3. y = 3 x − 4 y − 3 x = 1 table with 2 rows and 1 column , row1 column 1 , y equals 3 x minus 4 , row2 column 1 , y minus 3 x equals 1 , end table
4. y = 3 x − 14 y − x = 10 table with 2 rows and 1 column , row1 column 1 , y equals 3 x minus 14 , row2 column 1 , y minus x equals 10 , end table

Solve each system using substitution.

5. y = 2 x + 5 y = 6 x + 1 table with 2 rows and 1 column , row1 column 1 , y equals 2 x plus 5 , row2 column 1 , y equals 6 x plus 1 , end table
6. x = y + 7 y − 8 = 2 x table with 2 rows and 1 column , row1 column 1 , x equals y plus 7 , row2 column 1 , y minus 8 equals 2 x , end table
7. 4 x + y = 2 3 y + 2 x = − 1 table with 2 rows and 1 column , row1 column 1 , 4 x plus y equals 2 , row2 column 1 , 3 y plus 2 x equals negative 1 , end table
8. 4 x + 9 y = 24 y = − 1 3 x + 2 table with 2 rows and 1 column , row1 column 1 , 4 x plus 9 y equals 24 , row2 column 1 , y equals negative , 1 third , x plus 2 , end table

Solve each system using elimination.

9. 2 x + 5 y = 2 3 x − 5 y = 53 table with 2 rows and 1 column , row1 column 1 , 2 x plus 5 y equals 2 , row2 column 1 , 3 x minus 5 y equals 53 , end table
10. 4 x + 2 y = 34 10 x − 4 y = − 5 table with 2 rows and 1 column , row1 column 1 , 4 x plus 2 y equals 34 , row2 column 1 , 10 x minus 4 y equals negative 5 , end table
11. 11 x − 13 y = 89 − 11 x + 13 y = 107 table with 2 rows and 1 column , row1 column 1 , 11 x minus 13 y equals 89 , row2 column 1 , negative 11 x plus 13 y equals 107 , end table
12. 3 x + 6 y = 42 − 7 x + 8 y = − 109 table with 2 rows and 1 column , row1 column 1 , 3 x plus 6 y equals 42 , row2 column 1 , negative 7 x plus 8 y equals negative 109 , end table

Write and solve a system of equations to solve each problem. Explain why you chose the method you used.

13. Geometry The length of a rectangle is 3 times the width. The perimeter is 44 cm. What are the dimensions of the rectangle?
14. Farming A farmer grows only pumpkins and corn on her 420-acre farm. This year she wants to plant 250 more acres of corn than pumpkins. How many acres of each crop should the farmer plant?
15. Coins You have a total of 21 coins, all nickels and dimes. The total value is $1.70. How many nickels and how many dimes do you have?
16. Business Suppose you start an ice cream business. You buy a freezer for $200. It costs you $.45 to make each single-scoop ice cream cone. You sell each cone for $1.25. How many cones do you need to sell to break even?

Do you UNDERSTAND?

Reasoning Without solving, tell which method you would choose to solve each system: graphing, substitution, or elimination. Explain your answer.

17. y = 2 x − 5 4 y + 8 x = 15 table with 2 rows and 1 column , row1 column 1 , y equals 2 x minus 5 , row2 column 1 , 4 y plus 8 x equals 15 , end table
18. 2 y + 7 x = 3 y − 7 x = 9 table with 2 rows and 1 column , row1 column 1 , 2 y plus 7 x equals 3 , row2 column 1 , y minus 7 x equals 9 , end table
19. Reasoning If a system of linear equations has infinitely many solutions, what do you know about the slopes and y-intercepts of the graphs of the equations?
20. Open-Ended Write a system of equations that you would solve using substitution.
21. Reasoning Suppose you write a system of equations to find a break-even point for a business. You solve the system and find that it has no solution. What would that mean in terms of the business?

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