Download Name - Garnet Valley School

Algebra IIA
Algebra/Geometry Review: Systems of Equations and Inequalities

Foundational Material
o Ability to solve one step and multiple step
equations and inequalities
 Goal
o Find solutions that satisfy
systems of equations
o Ability to graph linear equations on a
coordinate plane
o Find solutions that satisfy
systems of inequalities

Why?
o Build a foundation for higher level mathematics
o Solve equations in Economics and Chemistry
o Determine which purchases are better deals

Key Vocabulary
o Consistent system
o Dependent system
o Inconsistent system
o Linear inequality
o System of equations
o Graph one or more
inequalities on a coordinate
plane
o System of
inequalities
o Solution to a system
Lesson 2: Applications with Systems of Equations

Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of
linear equations in two variables. (CC.9-12.REI.6)
 Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values,… (CC.9-12.REI.11)
 Create equations in two or more variable to represent relationships between quantities; graph equations
on coordinate axes with labels and scales.* (CC.9-12.CED.2)
 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and
interpret solutions as viable or nonviable options in a modeling context. (CC.9-12.CED.3)
Warm-Up:
The UPS truck brought 8 small boxes and 5 large boxes to your door. The total shipping charges for the boxes
was $184. One large box and one small box cost $29. Determine the cost to ship one of each size box.
You are at Starbucks ordering your favorite espresso drink. You notice that the barista is combing two types of
syrup. Container A is labeled 20% mocha chocolate syrup. Container B is labeled 50% dark chocolate syrup.
The size of the pitcher in 6 liters and the owner want the barista to mix the two syrups together to get 6 liters
that has 35% syrup. How many liters of each type of syrup must be used?
You are at the bank removing money to shop for holiday gifts. You deposited $270, part earning 2.5% interest
and the other part earning 3% interest. The total interest earned was $29. How much did you initially invest at
each rate?
The difference between two numbers is 11. Twice the smaller number plus three times the larger number is
123. What are the numbers?
A chemist has one solution that is 25% acid and a second that is 50% acid. How many liters of each should be
mixed to get 10 L of a solution that is 40% acid?
The perimeter of a rectangular field is 628 m. The length of the field exceeds its width by 6 m. Find the
dimensions
One week a business sold 40 scarves. White ones cost $4.95, and printed ones cost $7.95. In all $282 worth of
scarves were sold. How many of each kind were sold?
The measure of one of two supplementary angles is 8° more than three times the other. Find the measure of the
larger of the two angles. Hint: Supplementary angles sum to 180 degrees.