1. Drill # 95 Graph the following linear equations (on the same graph)
1. y = x + 2
2. y = x + 4
3. y = -x + 2

2. Launch
Troy has 10 bills in his pocket, all 5’s and 10’s. If the total amount that he has adds up to $70, how many of each bill (5’s and 10’s) does he have?
Write an equation that represents this situation…graph the equations…find the solution.

3. 5-1 Graphing Systems of Equations
Objective: To determine whether a system of equations has one, none, or infinitely many solutions.
OPEN BOOKS to page 253

4. (1.) Systems of Equations**
Definition: A set of equations with the same variables.
Example:
x + y = 2
3x – 2y = 6
How many solutions does this system have?
What is a solution to system of equations?

5. (2.) Consistent and (3.) Inconsistent**
Consistent: A system of equations that has at least one ordered pair that satisfies both equations.
(consistent means there is a solution)
Inconsistent: A system of equations that has no ordered pair that satisfies both equations.
(inconsistent means no solution)

6. (4.)Dependent and (5.) Independent**
Independent: A system that has exactly one solution.
Dependent: A system of equations that has infinitely many solutions.
All consistent systems of equations are either dependent (infinitely many solutions) or independent (one solution)

7. Possible solutions for systems of Equations*
Graphs of Equations
Number of Solutions
Terminology
Intersecting lines
Exactly one
consistent and independent
Same line
Infinitely many
consistent and dependent
Parallel lines
None
inconsistent

8. Number of Solutions* If a system has one solution, name it.
Example 1 a,b: page 254
Check your progress: page 254
Study Guide: #1-#4

9. Graphing Linear Equations*
Slope Intercept Form: y = mx + b
1. Plot the y-intercept (b)
2. Use the slope (rise/run) to find a second point
3. Draw a line through the points
Standard Form: Ax + By = C
1. Find the x and y intercepts (sub y=0 to find x-intercept, x=0 to find y-intercept)
2. Draw a line through the points

10. To solve a system of equations* (by graphing)
1. Graph both equations on the same coordinate plane.
2. Determine solution:
If they are parallel (same slope): no solution
If they are the same line (same slope and y- intercept): infinitely many solutions
If they intersect at one point: one solution