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Ch. 7 – Matrices and Systems of Equations 7.2 - Elimination
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Ex: Solve the system. Since both equations are in Ax + By = C form, use elimination. Multiply each equation by a number to get opposite variable amounts Because there are an opposite amount of y’s, we will add the equations together to cancel the y’s! Solve the remaining equation for x to get… x=1. But we need an answer in the form of (x, y)… I still need a y, so plug 1 in for x and solve for y! y=2, so the answer is (1, 2)! 7() 2( ) Elimination
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Solve the system: 1. (6, 3) 2. (-3, 6) 3. (-18, 11) 4. (-5, 3) 5. No Solution 6. Infinite Solutions
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Solve the system: 1. (5, 2) 2. (6, -1.5) 3. (10, -1) 4. (0, 5) 5. No Solution 6. Infinite Solutions
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Solve the system: 1. (0, 7/3) 2. (7, 0) 3. (7/4, 7/4) 4. (5, 3) 5. No Solution 6. Infinite Solutions
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Ex: Al has 19 coins, all dimes or quarters. The total amount of change he has is $2.65. How many dimes does Al have? We have 2 variables (# dimes and # quarters), so set up a system of equations! 1 st eqn: the total number of coins… 2 nd eqn: the total cost of the coins… Solve by elimination! So d = 14! Answer: 14 dimes -.25( )
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If a calculator is allowed, solve any system of equations by graphing! Ex: Solve this system by graphing. Solve both equations for y… …then graph and find all intersections! Answer: (7.991, 1.019)
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