SYSTEMS

Solution to a System An ordered pair that works in ALL equations of the system **The point at which the x and y value are the same.

Since the x and y values must be the same in both equations, then the x and y values are equal in both equations

Since the x and y values must be the same in both equations, then the x and y values are equal in both equations Since that is true, then both of these equations are equal to the same thing!!

Since the x and y values must be the same in both equations, then the x and y values are equal in both equations Since that is true, then both of these equations are equal to the same thing!! If two things are equal to the same thing, then they are equal to each other!!

To solve a system in which both equations are equal to the same thing, set them equal to each other.

Since x = 3, substitute into one equation and solve for y

Conclusion For the system: The solution to the system is x = 3, y = 6

Writing Solutions 1. Can be written as a coordinate pair (3, 6) 2. Can be individually identified x = 3, y = 6 3. May NOT just be written 3 6 - which is x? - is this 36??

Solve. Give the solution.

More Examples

Story Problem You purchase 8 gallons of paint and 3 brushes for $152.50. The next day you buy 3 gallons of paint and one brush for $56.50. How much does each gallon of paint and each brush cost?

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Assignment 7.2: 2 – 40 (evens)