3 Mid-Chapter Quiz

Do you know HOW?

Solve each system by graphing.

1. { 3 x − y = 8 10 + 2 y = 4 x left brace . table with 2 rows and 1 column , row1 column 1 , 3 x minus y equals 8 , row2 column 1 , 10 plus 2 y equals 4 x , end table
2. { y + 5 = 2 x 3 y + 6 x = − 3 left brace . table with 2 rows and 1 column , row1 column 1 , y plus 5 equals 2 x , row2 column 1 , 3 y plus 6 x equals negative 3 , end table
3. { 14 x − 2 y = 6 6 y − 9 x = 15 left brace . table with 2 rows and 1 column , row1 column 1 , 14 x minus 2 y equals 6 , row2 column 1 , 6 y minus 9 x equals 15 , end table

Without graphing, classify each system as independent, dependent, or inconsistent.

4. { 3 y + 2 x = 12 36 − 9 y = − 6 x left brace . table with 2 rows and 1 column , row1 column 1 , 3 y plus 2 x equals 12 , row2 column 1 , 36 minus 9 y equals negative 6 x , end table
5. { − 2 y = 20 − 2 x 3 y − 6 x = − 30 left brace . table with 2 rows and 1 column , row1 column 1 , negative 2 y equals 20 minus 2 x , row2 column 1 , 3 y minus 6 x equals negative 30 , end table
6. { 15 x = 10 y − 20 18 + 9 x = 6 y left brace . table with 2 rows and 1 column , row1 column 1 , 15 x equals 10 y minus 20 , row2 column 1 , 18 plus 9 x equals 6 y , end table

Solve each system by substitution.

7. { 5 m − n = 7 3 + 3 n = 6 m left brace . table with 2 rows and 1 column , row1 column 1 , 5 m minus n equals 7 , row2 column 1 , 3 plus 3 n equals 6 m , end table
8. { 4 y − 6 = 2 x y − 3 x = 9 left brace . table with 2 rows and 1 column , row1 column 1 , 4 y minus 6 equals 2 x , row2 column 1 , y minus 3 x equals 9 , end table
9. { 3 u + 8 = 4 v 24 v = 6 − 3 u left brace . table with 2 rows and 1 column , row1 column 1 , 3 u plus 8 equals 4 v , row2 column 1 , 24 v equals 6 minus 3 u , end table

Solve each system by elimination.

10. { 5 c − 4 t = 8 14 + 4 t = 3 c left brace . table with 2 rows and 1 column , row1 column 1 , 5 c minus 4 t equals 8 , row2 column 1 , 14 plus 4 t equals 3 c , end table
11. { 8 y + 10 = 6 x 8 y − 4 x = − 12 left brace . table with 2 rows and 1 column , row1 column 1 , 8 y plus 10 equals 6 x , row2 column 1 , 8 y minus 4 x equals negative 12 , end table
12. { 11 − 2 c = 3 d 2 c − 7 d = − 9 left brace . table with 2 rows and 1 column , row1 column 1 , 11 minus 2 c equals 3 d , row2 column 1 , 2 c minus 7 d equals negative 9 , end table

Graph the solutions to each of the following systems.

13. { y < 2 + 3 x y ≥ | x − 3 | left brace . table with 2 rows and 1 column , row1 column 1 , y less than 2 plus 3 x , row2 column 1 , y greater than or equal to vertical line x minus 3 vertical line , end table
14. { 2 x + y > 7 x < 4 y ≤ 5 left brace . table with 3 rows and 1 column , row1 column 1 , 2 x plus y greater than 7 , row2 column 1 , x less than 4 , row3 column 1 , y less than or equal to 5 , end table

Do you UNDERSTAND?

15. Which equation below combines with the equation − 4 x + 6 y = 3 negative 4 x plus 6 y equals 3  to form a system with an infinite number of solutions?
    1. 0.5 + x = 1.5 y
    2. 0.75 + 2x = 1.5 y
    3. 0.5 + 2x = 1.5 y
    4. 0.75 + x = 1.5 y

16. Write a system of inequalities to describe the shaded region.

    

17. An ordinary refrigerator costs $503 and has an estimated annual operating cost of $92. An energy-efficient model costs $615 with an estimated annual operating cost of $64. Write a system of equations to represent this situation.
    1. What is the solution of the system?
    2. What does the solution mean?
    3. Which model would you choose for your family? Why?
18. Writing Explain how to classify a linear system as independent, dependent, or inconsistent without graphing.

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