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Topics:
• Linear Inequalities
• Systems of Linear Equations
• Inequalities
MAT 150 Algebra
Class #7
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) and its total cost by C(x) , 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)?
Sec 2.3 – Systems of Equations
Steps for the Graphing Calculator:1. Put equations into y= screen2. Hit Zoom Fit (#0)3. Adjust window to see
intersection4. Hit 2nd TRACE and choose #55. Hit ENTER 3 times6. 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 and its total cost by , 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 B. 3x = y
x = -12y x - 2y = 26
Elimination/CombinationElimination/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 B. -5x + 8y = 16
2x – 5y = 6 12x + 24y = 15
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?
Investments
Sec 2.4 – Solutions of Linear InequalitiesInequality Signs
There are 4 inequality signs
> Greater than
≥ Greater than or Equal to
< Less than
≤ Less than or Equal to
Fill in the blank:
1. -2 ____ 4
2. 4 _____ 5
True or False:
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:
• – 15 2x - 3
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