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Algebra II Notes – 3.1 Solving Linear Systems By Graphing System of Two Linear Equations – Equations of two lines in the form Ax + By = C and Dx + Ey = F. Solution – a point (x, y) that satisfies both equations in the system. Two Lines in a Plane Can Do One of Three Things: 1.) Intersect at exactly one point. 2.) Do not intersect (parallel lines). 3.) The two lines coincide (are the same line). (one solution) (no solution) (infinite number of solutions.) EX: Solve the system by graphing: (First solve both equations for y, then graph both lines. Determine the point where the lines cross.) ⎧ x − y = −4 ⎨ ⎩x + y = 2 4 2 -5 5 -2 -4 What is the downside of solving by graphing? EX: Solve each by graphing: 4 ⎧2 x + y = 13 a.) ⎨ ⎩5 x − 2 y = 1 2 -5 5 -2 -4 ⎧2 x + 4 y = 12 b.) ⎨ ⎩x + 2 y = 6 4 2 -5 5 -2 -4 c.) ⎧x − y = 5 ⎨ ⎩2 x − 2 y = 9 4 2 -5 5 -2 -4 Day 1: Assign p. 142 #11 – 31 Odd Day 2: Assign p. 142 #32 – 34, 41, 42, 44, 46, 47, 51, 54