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# Solving Systems of Equations using Elimination

## 1. Solving Systems of Equations using Elimination

INF-21Botakul Bakdaulet

## 2.

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.

## 3. Example #1:

x + y = 105x – 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

## 4.

x + y = 105x – 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).

## 5.

x + y = 105x – y = 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

## 6. NOW solve these using elimination:

1.2.

2x + 4y =1

x - 4y =5

2x – y =6

x+y=3

## 7. Using Elimination to Solve a Word Problem:

Two angles are supplementary. Themeasure of one angle is 10 degrees

more than three times the other.

Find the measure of each angle.

## 8. Using Elimination to Solve a Word Problem:

Two angles are supplementary. Themeasure 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

## 9. Using Elimination to Solve a Word Problem:

Two angles are supplementary. Themeasure of one angle is 10 more

than three times the other. Find the

measure of each angle.

x + y = 180

x =10 + 3y

## 10. Using Elimination to Solve a Word Problem:

Solvex + 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)

## 11. Now you Try to Solve These Problems Using Elimination.

Solve1. Find two numbers whose sum is

18 and whose difference is 22.

2. The sum of two numbers is 128

and their difference is 114. Find

the numbers.