1. 3.1 Solving Systems of Equations by Graphing
Goals: ~Solve systems of equations by graphing
~Determine whether a system is consistent and independent, consistent and dependent, or inconsistent

2. Terms
System of Equations:Two or more equations with the same variables
Consistent: Has at least 1 solution
Independent: Exactly one solution
Dependent: Infinite number of solutions
Inconsistent: No solution

3. Pictures Consistent and Independent Inconsistent
Consistent and Dependent

4. Example 1: Solve by graphing
2x+y = 5
x – y = 1
Answer: Write each equation in slope-intercept form.
2x+y=5 --> y=-2x+5
x- y = 1 --> -y=-x+1 --> y=x-1
Graph. (Graph y-int then follow the slope[rise/run] to get the next point)
The point where they cross is the solution

5. Graph
(2,1) is the
solution.

6. Example 2: Solve by graphing and describe as consistent and independent, cons. and dependent, or inconsistent

7. Graph
Solution is
(2,1)

8. Answer:
They cross only once, so the graphs are consistent and independent

9. y = -x + 3 2y = -2x + 6 Solution : y = -x + 3
Example 2a: Without graphing, describe as consistent and independent, cons. and dependent, or inconsistent
y = -x + 3
2y = -2x + 6
Solution :
Put in slope-intercept form
Graph using
y-int and slope
y = -x + 3

10. Answer
They both make the same graph, so they are consistent and dependent!!! 

11. Without graphing, describe as consistent and independent, cons
Without graphing, describe as consistent and independent, cons. and dependent, or inconsistent
2a. y = 3x + 2
y = 3x -5
2b y = ½ x -6
y = 4x + 10

12. Mr. Frazer bought 2 lbs of cheddar cheese and 3 lbs of turkey
Mr. Frazer bought 2 lbs of cheddar cheese and 3 lbs of turkey. He paid $ Mrs. Cooper paid $18.35 for 1.5 lbs of cheese and 2 lbs of turkey. What was the price per pound of each item?