Advanced Algebra 2: Unit 10 Review
Name__________________ Hour__
For the unit 10 exam, you should be able to do the following:
• Use some or all of following methods to solve a system of two or three equations: substitution, elimination,
graphing, Cramer’s Rule, matrices. Remember that not all systems are linear. Calculators can be used, but be
sure you can solve without relying solely on your calculator.
• Solve a system of inequalities.
• Recognize when a system has no solution, one (or more) solutions, or infinite solutions.
• Identify which methods can/cannot be used for solving a system
• Set up a system of two or three equations that can be used to solve a real life situation.
The following problems are suggested for review:
⎧ 3x − 4y = 4 ⎫
⎪
⎪
1. ⎨
1 ⎬
⎪⎩ x − 3y = 2 ⎪⎭
⎧ x + 2y − z = 6
⎫
⎪
⎪
4. ⎨2x − y + 3z = −13 ⎬
⎪ 3x − 2y + 3z = −16 ⎪
⎩
⎭
⎧ 3x − 2y = 8 ⎫
⎪
⎪
2. ⎨
2
⎬
⎪⎩ x − 3 y = 12 ⎪⎭
⎧ y = 2x − 5 ⎫
3. ⎨
⎬
⎩ x = 3y + 4 ⎭
⎧2x + y + 3 = 0 ⎫
5. ⎨ 2
⎬ 2
⎩x + y = 5 ⎭
⎧⎪ 4y − x 2 = 1 ⎫⎪
6. ⎨ 2
⎬ 2
⎩⎪ y + x = 4 ⎭⎪
⎧−2x + y ≤ 2 ⎫
7. ⎨
⎬ ⎩x + y ≥ 2 ⎭
⎧ x 2 + y 2 ≤ 16 ⎫
8. ⎨
⎬ ⎩x + y ≥ 2 ⎭
⎧x ≥ 0
⎫
⎪y ≥ 0
⎪
⎪⎪
⎪⎪
9. ⎨ x + y ≥ 1
⎬
⎪ 3x + 2y ≤ 12 ⎪
⎪
⎪
⎪⎩ x + 3y ≤ 12 ⎪⎭
10. The band and orchestra are attending a concert. The band bought 16 student tickets and 3 adult tickets for
$110.50. The orchestra bought 12 student tickets and 4 adult tickets for $96. Find the cost of each type of ticket.
11. Mabel’s Mini Golf has different prices for seniors, adults, and children. Use the chart below to find the cost of
each type of ticket.
Number of Seniors
Number of Adults
Number of Children
Revenue
6:00 PM-7:00 PM
5
10
12
$310
7:00 PM-8:00 PM
5
5
4
$155
8:00 PM-9:00 PM
4
2
3
$92