1. 3.1 Graphing Systems of Equations
Learning goals
create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales
solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables
explain why the x-coordinates of the points where the graphs of equations f(x) and g(x) intersect are the solutions of the equation f(x)=g(x)
represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context

2. Vocabulary
systems of equations : two or more equations that use the same variables
solution : the set of values that makes ALL equations true

3. Intersecting Lines Same Line Parallel Lines One Solution
Consistent (intersecting)
Independent (one solution)
Y-intercept :
same or different
Slope : different
Infinitely many solutions
Consistent (intersecting)
Dependent (more than one solution)
Y-intercept : same
Slope: same
No solutions
Inconsistent (do not intersect)
Y-intercept : different
Slope: same

4. Solve by Graphing Solve by Substitution Solve by Elimination
Graph the first equation in slope-intercept form
Repeat step 1 with the other equation
Identify the point where the lines overlap
YOUR ANSWER SHOULD BE AN ORDERED PAIR
Special Cases:
No solution
Parallel Lines
Infinitely many
Same Line

5. Ex 1
Classify without graphing

6. Ex 2
Classify without graphing

7. Ex 3

8. Ex 4

9. Ex 5 Consider these questions
Is it possible for a system of equations to be both independent and inconsistent? Explain.
In a system of linear equations, the slope of one line is the negative reciprocal of the slope of the other line. Classify this system. Explain.

10. Ex 6
Determine whether each statement is always, sometimes or never true for the following system.
If m = 1, the system has no solution.
If m doesn’t = 1, the system has no solution.

11. Homework
Pg 138 #7-12, odd, 29, 30 on graph paper