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**8-1 Solve Systems by Graphing**

9P9: Solve 2X2 systems graphically

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**Possible outcomes of 2 lines**

They cross (intersect) in one place: 1 solution 2) They do not cross (Parallel): No Solution They coincide (same equation): infinite number of solutions

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**Why? If you want to compare to cell phone plans based**

on (minutes, Cost). What does the point where they cross represent? Minutes and cost are the same Which charges less per minute? Verizon, line not as steep How much does AT&T charge for activation? $0 AT&T Verizon

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**Example 1: Is (1,2) solution to this system?**

for y = x & x + y = 4 2 = (1) + 2 = 4 2=2 yes =4 4 = 4 yes So (1,2) is a solution to this system

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**Example 2: Is (-3,2) solution to the system?**

a + b = & b + 3a = 4 = (-3) =4 -1 = -1yes (-9) = 4 -7 = 4 no So (-3,2) is not a solution to this system

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**Ex 3: Find Solution by graphing Hint: Find point(s) of intersection**

x + y = 3 and x – y = 1 -x x y = -x + 3 -1 + y y x -1 = y The solution is (2,1)

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**Ex 4: y – 2x = 3 & y = 2x - 2 +2x +2x y = 3 + 2x**

Hey when they have the same slopes they are parallel and don’t cross. That means there is no solution!!

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Ex 5: 3y - 2x = & +2x x 3y = 6 + 2x Hey, these are the same line so all the points are the same or infinite # of solutions

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**Find solutions by graphing**

Ex 6: x + 2y =7 & x = y + 4 Remember to solve for y! -x x 2y = 7- x x - 4 = y The solution is (5,1)

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Assignment 8-1/ /8-28 even,32, 40-46

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MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.

MATH 416 Equations & Inequalities II. Graphing Systems of Equations The graphic method to solve a system of equations consists in determining the coordinates.

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