Solving Systems of Equations using Elimination презентация

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)