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Solve Systems of Equations By Graphing VOCABULARY • A system of two linear equations, also called a linear system, in two variables x and y consists of two equations that can be written in the following form: Ax + By = C Dx + Ey = F VOCABULARY • A solution of a system of linear equations in two variables is an ordered pair (x, y) that satisfies both equations. – At least 1 solution: CONSISTENT – No solutions: INCONSISTENT [graph is parallel lines] – Exactly 1 solution: INDEPENDENT – Infinitely many solutions: DEPENDENT VOCABULARY • CONSISTENT INDEPENDENT • CONSISTENT DEPENDENT • INCONSISTENT EXAMPLES 1) Check whether the ordered pair is a solution of the systems. a. (7, 4) y + x = 11 y – 2x = -10 EXAMPLES 1) Check whether the ordered pair is a solution of the systems. b. (1, 5) 3x - 2y = 7 y = 2x + 1 EXAMPLES 2) Graph the linear system and estimate the solution. Then check the solution algebraically. a. y = –3x + 5 y = 2x – 5 EXAMPLES 2) Graph the linear system and estimate the solution. Then check the solution algebraically. b. 3x + y = 7 y = 2x - 3 EXAMPLES 3) Graph the linear systems. Then classify as consistent & independent, consistent & dependent, or inconsistent. a. 4x + 3y = 9 -2x +3y = -6 EXAMPLES 3) Graph the linear systems. Then classify as consistent & independent, consistent & dependent, or inconsistent. b. -x + y = 3 y=x-7