Chapter 6 Study Guide
Systems of Equations
Name ______________________________
Period _________
1) Explain what it means for a point to be a solution to a system of equations.
2) Determine if the point is a solution to each of the system.
a) y = -3x – 3
b) y = -2x – 9
c) y = -2x + 4
3x - 2y = -3
4x - y = -9
-3x - 3y = -3
(-1,0)
(1,2)
(3,-2)
d) -x - 4y = 5
2x + y = -3
(-5,0)
3) Given the following scenario and graph answer each question.
There are two main phone plans that you can choose from. Plan A costs $55 a month plus $5 for each gigabyte
of data. Plan B costs $35 a month plus $10 a month for each gigabyte of date.
a) Sarah uses 2 GB how much will she pay for each plan?
b) Sam uses 8 GB how much will she pay for each plan?
c) Suh uses 4 GB how much will she pay for each plan?
d) Seth uses 3 GB of data. Recommend a plan and explain
your reasoning
4) Draw an example of a system that has 1, 0, & ∞ solutions.
5) Determine the solution using the Graphing method.
𝑦 = 3𝑥 − 4
a.
1
𝑦 =− 𝑥+3
𝑥+𝑦 =1
b.
2
c.
1
𝑦 = 𝑥−3
3
𝑦=3
𝑦 = 2𝑥 − 1
d.
𝑥+𝑦 =3
𝑥+𝑦 =5
6) Determine the solution using the Substitution method.
a.
𝑥 = −3𝑦 + 1
𝑥+𝑦 =5
b.
−2𝑥 + 𝑦 = 8
𝑦 = 6𝑥
c.
𝑦 = −5
𝑦 = 2𝑥 − 1
d.
2𝑥 + 2𝑦 = 24
𝑦 = 4𝑥 + 2
d.
−4𝑥 + 9𝑦 = 9
𝑥 − 3𝑦 = −6
7) Determine the solution using the Elimination method.
a.
3𝑥 + 1𝑦 = −4
−3𝑥 + 1𝑦 = −6
b.
3𝑥 + 6𝑦 = 9
2𝑥 − 6𝑦 = 6
c.
8𝑥 + 𝑦 = −16
−3𝑥 + 𝑦 = −5
8) Mario is selling Scarf’s in his new online clothing store. He has developed
Using any method, determine how many scarfs he has to sell in order to break even. Show work.
a)
b)
Cost: 𝑦 = 5𝑥 + 80
Cost: 𝑦 = 100
Revenue: 𝑦 = 15𝑥
Revenue: 𝑦 = 10𝑥 + 15
9) Last week, Kelly did 2 loads of laundry and 7 loads of dishes, and her parents paid her $18.
The week before, she finished 2 loads of laundry and 4 loads of dishes, earning a total of $12.
a) Define variables and write a system of equations for the scenario.
b) Determine the solution using any method.
c) Interpret the meaning of the solution.
10) The cats Killer and Croaker catch mice on the waterfront. Killer has already caught 20 mice and
catches 80 more mice each month. Croaker has already caught 100 mice and catches 40 more mice
each month.
a) Define variables and write a system of equations for the scenario.
b) Determine the solution using any method.
c) Interpret the meaning of the solution.
Review
11) Simplify/Evaluate each of the following
3
a. 𝑥 ∙ 𝑥
5
b.
(𝑥 6 )4
12) Solve for x
−2(𝑥 − 5) + 5 = 29
c.
15𝑦 8
𝑥 4 ∙𝑥 3
d.
(𝑥 −2 )−5
20𝑦 2
𝟑 −𝟐
e) ( )
𝒙
13) Evaluate the fraction
a)
3
2
4
+ =
b)
5
2 5
∙ =
9 3
Sketch a Graph and identify key info (slope , x-int, y-int):
2
(39) 2𝑥 − 3𝑦 = 12
(40) 𝑦 = 𝑥 + 1
5
Find the Slope
(43)
(17, 5) & (22 , 11)
(44)
(11, -5) & (6 , 2)
Given the parent function 𝒇(𝒙) = 𝟐𝒙 write a function for each description.
(6) 𝑈𝑝 2 𝑢𝑛𝑖𝑡𝑠
(7) 𝐿𝑒𝑓𝑡 4 𝑢𝑛𝑖𝑡𝑠
(8) 𝐹𝑙𝑖𝑝 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙𝑦