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

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

Points of Intersection System Outcomes Lines Points of Intersection Slope y-Intercept Classification Intersecting 1 different same or different Independent parallel same Inconsistent coinciding infinitely many Dependent

Ex 1 Classify without graphing

Ex 2 Classify without graphing

Ex 3

Ex 4

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.

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.