 # Systems of Equations and Inequalities in Two Variables A-REI.3; A-REI.5; A-REI.6; A-REI.7.

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Systems of Equations and Inequalities in Two Variables A-REI.3; A-REI.5; A-REI.6; A-REI.7

EQ: How Do Solve Systems of Equations with the Graphing Method ? 8/7/2015

System of Equations A collection of 2 or more lines, including nonlinear equations

Solution to a system The ordered pair (or set of points) that satisfy all equations in the system, at the same time Called the point of intersection There are three different types: no solution, infinite solutions, one solution

One Solution The two lines cross each other in exactly one point on the graph Infinite Solutions The two lines on the graph lie on top of each other. No Solution The two lines never cross. a = b x = a a = a

Example 1: Find the solution to given system: y = -1x +3 y = 1x – 3 2 Solution: (4, -1)

Guided Practice 1 Find the solution to given system: y = 2x – 5 y = -3x + 2 2 Solution: (2, -1)

Guided Practice 2 Find the solution to given system: y = – 5 y = -4x + 3 Solution: (2, -5)

Guided Practice 3 Find the solution to given system: y = 2x – 6 y = 1x + 2 4 Solution: (4, -3)

Questions How many times do the lines cross in order to have one solution? What does having a solution mean? What does every line need to have when drawn?

Example 2: Find the solution to given system: y = 2x + 4 y = 6x 3 Solution: No Solution

Guided Practice 4 Find the solution to given system: x – y = 4 -5x + 5y = -20 x – y = 4 -x -y = -x + 4 __ -1 y = x - 4 -5x + 5y = -20 +5x ____________ 5y = 5x – 20 __ 5 y = x – 4 y = x - 4 y = x – 4 Solution: Infinite Solutions

Guided Practice 5 Find the solution to given system: -4x + 8y = 16 6x – 3y = 12 -4x + 8y = 16 + 4x ______________ 8y = 4x + 16 __ 8 y = 1x + 2 2 -6x ____________ -3y = -6x + 12 __ -3 y = 2x – 4 y = -2x – 4 Solution: (4, 4)

Questions What variable do you need to solve for in order to graph? What will be the same in equations that have no solution? What will be the same in equations that have infinite solutions?

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