2VocabularyA system of linear equations in two variables x and y, also called a linear system, consists of two or more equations that can be written in the following form.Ax + By = CDx + Ey = FA solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation.
3The solution is the point of intersection which is (6, -1). Solve by GraphingExample 1.Solve by graphingy = -x + 5-2y = -3x + 20y = 3/2 x -10The solution is the point of intersection which is (6, -1).
4Classifying Systems System with at least one solution: is called Consistent.Exactly one solution is consistent - independentInfinitely many solutions is consistent - dependentSystem with no solution:is called Inconsistent.EX2.EX3.ConsistentIndependent(Intersecting)ConsistentDependent(Same graph)EX4.Inconsistent(Parallel)
5Practice GraphingSolve the system by graphing. Then classify the system as consistent and independent, consistent and dependent, or inconsistent.-2x +y = 5y = -x +22. 3x - 2y = 103x - 2y = 222x + 5y = 64x +10y = 12Infinitely many solution; Consistent and dependent(-1,3) Consistent and independentNo solution; inconsistent
6Graph systems of Linear Inequalities To graph a system of linear inequalities, follow these steps:Step 1 – Solve each inequality for y.Step 2 – Graph each inequality.Pick the type of lines (solid or dotted)Pick where to shade (above or below)Step 3 – Identify the region of the graph that is shaded for ALL of the inequalities