Solving Systems of Equations using Elimination INF-21 Botakul

Solving Systems of Equations using Elimination INF-21 Botakul Bakdaulet

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 #1: 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

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

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

Using Elimination to Solve a Word Problem: Two angles are supplementary. The measure of one angle is 10 degrees more than three times the other. Find the measure of each angle.

Using Elimination to Solve a Word Problem: Two angles are supplementary. The measure of one angle is 10 more than three times the other. Find the measure of each angle. x = degree measure of angle #1 y = degree measure of angle #2 Therefore x + y = 180

Using Elimination to Solve a Word Problem: Two angles are supplementary. The measure of one angle is 10 more than three times the other. Find the measure of each angle. x + y = 180 x =10 + 3y

Using Elimination to Solve a Word Problem: Solve x + y = 180 x =10 + 3y x + y = 180 -(x - 3y = 10) 4y =170 y = 42.5 x + 42.5 = 180 x = 180 - 42.5 x = 137.5 (137.5, 42.5)

Now you Try to Solve These Problems Using Elimination. Solve Find two numbers whose sum is 18 and whose difference is 22. The sum of two numbers is 128 and their difference is 114. Find the numbers.