7-3: Solving Systems of Equations using Elimination

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Step 1: Put the equations in Standard Form. Standard Form: Ax + By = C

Presentation transcript:

7-3: Solving Systems of Equations using Elimination Steps: 1. Place both equations in Standard Form, Ax + By = C. 2. Determine which variable to eliminate with Addition or Subtraction. 3. Solve for the variable left. 4. Go back and use the found variable in step 3 to find second variable. 5. Check the solution in both equations of the system.

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

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

5x + 3y = 11 5x = 2y + 1 5(1) + 3(2) =11 5(1) = 2(2) + 1 5 + 6 =11 Step 5: Check the solution in both equations. The solution to the system is (1,2). 5x + 3y = 11 5(1) + 3(2) =11 5 + 6 =11 11=11 5x = 2y + 1 5(1) = 2(2) + 1 5 = 4 + 1 5=5

Solving Systems of Equations using Elimination Steps: 1. Place both equations in Standard Form, Ax + By = C. 2. Determine which variable to eliminate with Addition or Subtraction. 3. Solve for the remaining variable. 4. Go back and use the variable found in step 3 to find the second variable. 5. Check the solution in both equations of the system.

Example #2: x + y = 10 5x – y = 2 Step 1: The equations are already in standard form: x + y = 10 5x – y = 2 Step 2: Adding the equations will eliminate y. x + y = 10 x + y = 10 +(5x – y = 2) +5x – y = +2 Step 3: Solve for the variable. x + y = 10 +5x – y = +2 6x = 12 x = 2

Solution to the system is (2,8). x + y = 10 5x – y = 2 Step 4: Solve for the other variable by substituting into either equation. x + y = 10 2 + y = 10 y = 8 Solution to the system is (2,8).

x + y =10 5x – y =2 2 + 8 =10 5(2) - (8) =2 10 – 8 =2 10=10 2=2 Step 5: Check the solution in both equations. Solution to the system is (2,8). x + y =10 2 + 8 =10 10=10 5x – y =2 5(2) - (8) =2 10 – 8 =2 2=2

NOW solve these using elimination: 1. 2. 2x + 4y =1 x - 4y =5 2x – y =6 x + y = 3

NOW solve these using elimination: 1. 2. 2x + 4y =1 x - 4y =5 2x – y =6 x + y = 3 Solution (2,- 3 4 ) Solution (3,0)