**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

**Regular Solving**

Purpose: Find the value of 1 variable.

**Example**

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?

**Equation**

16 +

k= 26, wherekis the weight of the kitten in pounds.

**Solving a System of Linear Equations**

Purpose: Find the value of 2 variables.

**Example**

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.

**Equations**

p+k= 180 (The puppy’s weight,p, plus the kitten’s weight,k.)3

p+ 2k= 414 (The sum of 3 times the weight of the puppy and twice the weight of the kitten.)