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Dr. Fowler CCM Solving Systems of Equations By Elimination – Easier

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Solving a system of equations by elimination using addition and subtraction. Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. Step 3: Add or subtract the equations. Step 4: Plug back in to find the other variable. Step 5: Check your solution. Standard Form: Ax + By = C Look for variables that have the same coefficient. Solve for the variable. Substitute the value of the variable into the equation. Substitute your ordered pair into BOTH equations.

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1) Solve the system using elimination. x + y = 5 3x – y = 7 Step 1: Put the equations in Standard Form. Step 2: Determine which variable to eliminate. They already are! The y’s have the same coefficient. Step 3: Add or subtract the equations. Add to eliminate y. x + y = 5 (+) 3x – y = 7 4x = 12 x = 3

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1) Solve the system using elimination. Step 4: Plug back in to find the other variable. x + y = 5 (3) + y = 5 y = 2 Step 5: Check your solution. (3, 2) (3) + (2) = 5 3(3) - (2) = 7 The solution is (3, 2). What do you think the answer would be if you solved using substitution? x + y = 5 3x – y = 7

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EXAMPLE #2: STEP 2:Use subtraction to eliminate 5x. 5x + 3y =11 5x + 3y = 11 -(5x - 2y =1) -5x + 2y = -1 5x + 3y = 11 5x = 2y + 1 Note: the (-) is distributed. STEP 3:Solve for the variable. 5x + 3y =11 -5x + 2y = -1 5y =10 y = 2 STEP1: Write both equations in Ax + By = C form. 5x + 3y =11 5x - 2y =1

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STEP 4: Solve for the other variable by substituting y = 2 into either equation. 5x + 3y =11 5x + 3(2) =11 5x + 6 =11 5x = 5 x = 1 5x + 3y = 11 5x = 2y + 1 The solution to the system is (1, 2).

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3) Solve the system using elimination. 4x + y = 7 4x – 2y = -2 Step 1: Put the equations in Standard Form. They already are! Step 2: Determine which variable to eliminate. The x’s have the same coefficient. Step 3: Add or subtract the equations. Subtract to eliminate x. 4x + y = 7 (-) 4x – 2y = -2 3y = 9 y = 3 Remember to “keep-change- change”

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3) Solve the system using elimination. Step 4: Plug back in to find the other variable. 4x + y = 7 4x + (3) = 7 4x = 4 x = 1 Step 5: Check your solution. (1, 3) 4(1) + (3) = 7 4(1) - 2(3) = -2 4x + y = 7 4x – 2y = -2

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4) Solve the system using elimination. y = 7 – 2x 4x + y = 5 Step 1: Put the equations in Standard Form. 2x + y = 7 4x + y = 5 Step 2: Determine which variable to eliminate. The y’s have the same coefficient. Step 3: Add or subtract the equations. Subtract to eliminate y. 2x + y = 7 (-) 4x + y = 5 -2x = 2 x = -1

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4) Solve the system using elimination. Step 4: Plug back in to find the other variable. y = 7 – 2x y = 7 – 2(-1) y = 9 Step 5: Check your solution. (-1, 9) (9) = 7 – 2(-1) 4(-1) + (9) = 5 y = 7 – 2x 4x + y = 5

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Elimination using Addition 5) Solve the system x - 2y = 5 2x + 2y = 7 Lets add both equations to each other

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Elimination using Addition 5) Solve the system x - 2y = 5 2x + 2y = 7 Lets add both equations to each other + NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

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Elimination using Addition 5) Solve the system x - 2y = 5 2x + 2y = 7 Lets add both equations to each other + 3x = 12 x = 4 ANS: (4, y) NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

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Elimination using Addition 5) Solve the system x - 2y = 5 2x + 2y = 7 ANS: (4, y) Lets substitute x = 4 into this equation. 4 - 2y = 5Solve for y - 2y = 1 y = 1 2 NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

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Elimination using Addition 5) Solve the system x - 2y = 5 2x + 2y = 7 Answer: (4, ) Lets substitute x = 4 into this equation. 4 - 2y = 5Solve for y - 2y = 1 y = 1 2 1 2 NOTE: We use the Elimination Method, if we can immediately cancel out two like terms.

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Elimination using Addition 3x + y = 14 4x - y = 7 NOTE: We use the Elimination Method, if we can immediately cancel out two like terms. 5) Solve the system

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Elimination using Addition 3x + y = 14 4x - y = 7 7x= 21 x = 3 ANS: (3, y) + 5) Solve the system

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Elimination using Addition Answer: (3, 5 ) 3x + y = 14 4x - y = 7 Substitute x = 3 into this equation 3(3) + y = 14 9 + y = 14 y = 5 NOTE: We use the Elimination Method, if we can immediately cancel out two like terms. 5) Solve the system

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Excellent Job !!! Well Done

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Stop Notes Do Worksheet

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