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Published byLouise O’Neal’ Modified over 7 years ago

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Sections 3.1 & 3.2

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A collection of equations in the same variables.

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The solution of a system of 2 linear equations in x and y is any ordered pair, (x, y), that satisfies both equations. The solution (x, y) is also the point of intersection for the graphs of the lines in the system.

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The ordered pair (2, -1) is the solution of the system below. y = x – 3 y = 5 – 3x

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Exploring Graphs of Systems YOU WILL NEED: graph paper or a graphing calculator

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System I.Y = 2x – 1 Y = -x + 5 II.Y = 2x – 1 Y = 2x + 1 III.Y = Y = x + 2 Graph System I at left. ◦ Are there any points of intersection? ◦ Can you find exactly one solution to the system? If so, what is it? Repeat for Systems II and III.

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I. Y = 2x – 1 Y = -x + 5 Plug in your equations to Y= Press Graph

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Press 2 nd, CALC Select 5: INTERSECT

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FIRST CURVE? Press Enter to select the line. SECOND CURVE? Press Enter to select the 2 nd line GUESS? Move the cursor close to the point of intersection and press Enter

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Intersection Point (2, 3)

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Graphing a system in 2 variables will tell you whether a solution for the system exists. 3 possibilities for a system of 2 linear equations in 2 variables.

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If a system of equations has at least 1 solution, it is called consistent ◦ If a system has exactly one solution, it is called independent (INTERSECTING) ◦ If a system has infinitely many solutions, it is called dependent (SAME LINE) (COINCIDING)

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If a system does not have a solution, it is called inconsistent. (PARALLEL LINES) (NO SOLUTION)

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Graph and Classify each system. Then find the solution from the graph. x + y = 5 x – 5y = -7 Begin by solving each equation for y.

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Graph and find the intersection point like Activity 1. y = 5 – x y = Consistent & Independent

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2x + y = 3 3x – 2y = 8 Solve the first equation for y.

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SUBSTITUTE 3 – 2x into the second equation for y. SOLVE

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Substitute 2 for x in either original equation to find y.

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Solution: (2, -1) Check:

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Involves multiplying and combining the equations in a system in order to eliminate a variable.

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Now plug in y = 1 into either of your two original equations.

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Pg 160-163 Pg 168-170

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