Download MAT 150 Algebra Class #4

Topics:
• Linear Inequalities
• Systems of Linear Equations
Sec 2.3 – Systems of Equations
Solving Systems by Graphing
A company is said to break even from the production and sale of
a product if the total revenue (incoming $) equals the total cost.
Suppose a company has its total revenue for a product given by
R(x) = 5585𝑥 and its total cost by C(x) = 61740 + 440𝑥, where
x is the number of thousands of tons of the product produced
and sold per year. When will the company break even or make
profit P(x)?
Steps for the Graphing Calculator:
1. Put equations into y= screen
2. Hit Zoom Fit (#0)
3. Adjust window to see intersection
4. Hit 2nd TRACE and choose #5
5. Hit ENTER 3 times
6. Interpret answer
Solving Systems with Substitution
Same Question –Different Method
A company is said to break even from the production and
sale of a product if the total revenue (incoming $) equals
the total cost. Suppose a company has its total revenue
for a product given by 𝑦 = 5585𝑥 and its total cost by 𝑦 =
61740 + 440𝑥, where x is the number of thousands of
tons of the product produced and sold per year. When will
the company break even?
Practice with Substitution
*look for the variable by itself
A. 2x – 3y = 6
x = -12y
B. 3x = y
x - 2y = 26
Elimination/Combination
Elimination/Combination is best used when both equations in the system are in
standard form (Ax + By = C)
This method combines both equations by adding them together, but one of the
variables must be eliminated as soon as the equations are combined.
4x – 2y = 7 * Are the equations in standard form?
x + 2y = 3
Forcing an Elimination
A. 4x + 9y = 2
2x – 5y = 6
B. -5x + 8y = 16
12x + 24y = 15
Investments
An investor has $300,000 to invest, part at 12%
and the remainder in a less risky investment at
7%. If her investment goal is to have an annual
income of $27,000, how much should she put in
each investment?
Sec 2.4 – Solutions of Linear Inequalities
Inequality Signs
There are 4 inequality signs
Fill in the blank:
> Greater than
1. -2 ____ 4
≥ Greater than or Equal to
2. 4 _____ 5
< Less than
True or False:
≤ Less than or Equal to
3. -5 ≤ -11
4. 21 > 12
Graphing Inequalities on a
Number Line
Graph the following on a number line:
X > -4
X≤7
>
OPEN Circles
<
≥
CLOSED Circles
≤
Solving Inequalities
Solve & Graph the following inequalities:
• 3𝑥 + 7 ≥ 13
•
1
3
3 − 2𝑥 < −4(𝑥 + 1)
• – 15 < 2x - 3 ≤ 1)
• 6𝑥 − 2 ≤ −4 or 3𝑥 + 4 > 9
Special Rule:
You MUST flip the inequality
sign when you multiply or
divide by a negative!
Graphing Double Inequalities:
“And” statements make a line
segment
“Or” statements go opposite of
each other or overlap
Inequalities in Real-Life
Course Average
To pass a course with a B average, a student must
have an average of 80% or greater. A student’s
grades on three tests are 75%, 83%, 72% and 86%.
What grade must the student earn on the final test so
that his course average is a B or better.
What would change if the student only wanted a B
average?
Assignment
Sec. 2.3 Pg. 134-136
#3-5 all
#11-17 odd (Must show work to receive any credit)
#25-29 odd (Must show work to receive any credit)
#42, 44, 52
Sec. 2.4 Pg. 146-149
#1-7 odd (Must show work to receive any credit)
# 13- 15 odd (Must show work to receive any credit)
#21-25 odd (Must show work to receive any credit)
#33