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Section_8_1_Notes

Section_8_1_Notes - Example 3 Solve 2x 2y = 6 by...

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Section 8.1 Systems of two equations and two unknowns: A*x + B*y = C D*x = E*y = F There are 3 methods to solve: 1.) Graphing – Sketch the graph of each line and see where they intersect (if they intersect) 2.) Substitution – Solve on equation for one of the variables and then substitute that into the other equation 3.) Elimination – Add multiples of each equation together to eliminate one of the variables

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If a system has at least one solution, then it is said to be consistent. If there is no solution, it is said to be inconsistent. If there are infinite solutions it is dependent. If not, they are independent. Consistent Consistent Inconsistent Independent Dependent Independent Example 1: Solve x - y = 5 by substitution 2x + y = 1
Example 2: Solve x – y = 3 by substitution 9x + 7y = -69

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Unformatted text preview: Example 3: Solve 2x + 2y = 6 by elimination 6x – 2y = -14 Example 4: Solve x + y = 2 and classify 2x + y = 0 Example 5: Solve 5x + 6y = 1 and classify 10x + 12y = 2 Example 6: Solve 2x + 3y = 4 and classify 4x + 6y = -4 Applications: Example 1: A motorboat takes 5 hours to make a trip downstream with a current of 2 mph. The return trip takes 7 hours. Find the speed of the boat in still water. Example 2: A coffee shop charges \$11 for Kenyan Roast Coffee and \$10 for Folgers Coffee. How much of each type should be used to make a 20 pound blend that sells for \$10.60 per pound? Example 3: The break even point is where the cost equals the revenue. Find the break even point if the cost is defined by C(x) = 10x + 450 and the revenue is defined by R(x) = 15x...
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Section_8_1_Notes - Example 3 Solve 2x 2y = 6 by...

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