Name ______Date ______Hour______
Chapter 3 Review
Algebra II
Choose the letter of the term that best matches each phrase.
1. ______A system of equations that has an infinite number of solutions
2. ______The region of a graph where every constraint is met
3. ______A method of solving equations in which one equation is solved
4. ______A system of equations that has at least one solution
5. ______A method of solving equations in which one variable is
eliminated when the two equations are combined
6. ______the solution of a system of equation in three variables
7. ______A system of equations that has no solution
8. ______A system of equations that has exactly one solution
9. ______Two or more equations with the same variables
10. ______The points where the maximum or minimum values will occur
Complete each section. Show ALL work.
Solve each system of equations by graphing.
11.3x + 2y = 12______12. 8x – 10y = 7______
x – 2y = 44x – 5y = 7
13. y – 2x = 8______
y = ½ x – 4
Solve each system of equations by substitution.
14. x + y = 5______15. x + y = 4______
2x – y = 4x – y = 8.5
Solve each system of equations by elimination.
16. -2x – 6y = 0______17. 3x – 5y = -13______
3x + 11y = 44x + 2y = 0
Solve each system of equations by the method of your choice.
18. 20y + 13x = 10______19. 2x – 3y = 9______
0.65x + y = 0.54x + 2y = -22
20. -7x + 6y = 42______21.2x + 6y = 6______
3x + 4y = 28⅓ x + y = 1
Solve each system of inequalities by graphing.
22. y 423.|x + 4| 3
y > -32y x + 4
24.y > x + 4
-2y x – 3
Graph each system of inequalities and name the coordinates of the vertices. Then find the maximum and minimum value of the given function.
25. y 5______
y -3
4x + y 5______
-2x + y 5
f(x,y) = 4x – 3y
Solve each system of equations with 3 variables.
26.x + 4y – z = 6______27. 2a + b – c = 5 ______
3x + 2y + 3z = 16a – b + 3c = 9
2x – y + z = 33a – 6c = 6
28. e + f = 4______
2d + 4e – f = -3
3e = -3
For questions 29 & 30, use the following information.
Last year the volleyball team paid $5 per pair for socks and $17 per pair for shorts on a total purchase of $315. This year they spent $342 to buy the same number of pairs of socks and shorts because the socks now cost $6 and the shorts cost $18.
29.Write a system of two equations that represents the number of pairs of socks and shorts bought each year.
______
______
30.How many pairs of socks and shorts did the team buy each year?
______