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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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**The solution is the point of intersection which is (6, -1).**

Solve by Graphing Example 1. Solve by graphing y = -x + 5 -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. EX2. EX3. Consistent Independent (Intersecting) Consistent Dependent (Same graph) EX4. Inconsistent (Parallel)

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Practice Graphing Solve the system by graphing. Then classify the system as consistent and independent, consistent and dependent, or inconsistent. -2x +y = 5 y = -x +2 2. 3x - 2y = 10 3x - 2y = 22 2x + 5y = 6 4x +10y = 12 Infinitely many solution; Consistent and dependent (-1,3) Consistent and independent No solution; inconsistent

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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**

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**Practice systems of inequalities**

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