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Solving Systems with 2 Variables U3.1

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Vocabulary A 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 = C Dx + Ey = F A solution of a system of linear equations in two variables is an ordered pair (x,y) that satisfies each equation.

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Example 1. Solve by graphing y = -x + 5 Solve by Graphing -2y = -3x + 20 y = 3/2 x -10 The solution is the point of intersection which is (6, -1).

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Classifying Systems System with at least one solution: is called Consistent. Exactly one solution is consistent - independent Infinitely many solutions is consistent - dependent System with no solution: is called Inconsistent. Consistent Independent (Intersecting) Consistent Dependent (Same graph) Inconsistent (Parallel) EX2.EX3. EX4.

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Practice Graphing Solve the system by graphing. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. 1.-2x +y = 5 y = -x x - 2y = 10 3x - 2y = x + 5y = 6 4x +10y = 12 (-1,3) Consistent and independent No solution; inconsistent Infinitely many solution; Consistent and dependent

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Graph 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

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Solve the system of Inequalities by graphing 4.

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Practice systems of inequalities 5.6.

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