Frustrated Student: “This is why I hate Algebra. I'm not going to use this; I’m going to become an actor.”
Patient Tutor: "You're right. Unless you're Russell Crowe in A Beautiful Mind or Matt Damon in Good Will Hunting, you can leave quadratic functions in the classroom. Patience, discipline, decision making skills - these are the lessons you learn from quadratic functions that you use in real life."
1. Systems of Equations Definitions
- System of linear quations: Two or more equations with two or more variables. When graphed, these lines intersect at some point (x, y). Note: This lesson focuses on systems of equations with 2 equations and 2 distinct variables.
- Intersection: The point (x,y) where the lines meet.
- Solution: The x and y value of the intersection of the 2 lines.
- No Solution: When graphed, sometimes the system of equations is actually a set of parallel lines. Because parallel lines never intersect, this system will have no solution.
- Infinite Number of Solutions: When graphed, this system of equations is actually the same line.
2. Systems of Linear Equations Differ from Regular Equations
Purpose: Find the value of 1 variable.
A puppy weighs 16 pounds. When a kitten sits on the scale with the puppy, the combined weight of the animals is 26 pounds. How much does the kitten weigh?
16 + k = 26, where k is the weight of the kitten in pounds.
Solving a System of Linear Equations
Purpose: Find the value of 2 variables.
The combined weight of a puppy and a kitten is 180 pounds. The sum of 3 times the weight of the puppy and twice the weight of the kitten is 414 pounds. Find the weight of each animal.
p + k = 180 (The puppy’s weight, p, plus the kitten’s weight, k.)
3p + 2k = 414 (The sum of 3 times the weight of the puppy and twice the weight of the kitten.)