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**Solve Systems of Equations By Graphing**

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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

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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

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VOCABULARY CONSISTENT INDEPENDENT CONSISTENT DEPENDENT INCONSISTENT

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EXAMPLES 1) Check whether the ordered pair is a solution of the systems. (7, 4) y + x = 11 y – 2x = -10

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EXAMPLES 1) Check whether the ordered pair is a solution of the systems. (1, 5) 3x - 2y = 7 y = 2x + 1

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EXAMPLES 2) Graph the linear system and estimate the solution. Then check the solution algebraically. y = –3x + 5 y = 2x – 5

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EXAMPLES 2) Graph the linear system and estimate the solution. Then check the solution algebraically. 3x + y = 7 y = 2x - 3

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EXAMPLES 3) Graph the linear systems. Then classify as consistent & independent, consistent & dependent, or inconsistent. 4x + 3y = 9 -2x +3y = -6

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EXAMPLES 3) Graph the linear systems. Then classify as consistent & independent, consistent & dependent, or inconsistent. -x + y = 3 y = x - 7

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