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3-2 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.

EXAMPLE 1

5x 3y 11 5x 2y 1

STEP1 Write both equations in Ax By C

form. 5x 3y 1

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

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

Step 5 Check the solution in both equations.

The solution to the system is (1,2).

5x 2y 1 5(1) 2(2) 1 5 4 1

55

5x 3y 11 5(1) 3(2) 11 5 6 11

1111

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

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

Step 5 Check the solution in both equations.

Solution to the system is (2,8).

x y 10 2 8 10 1010

5x y 2 5(2) - (8) 2 10 8 2

22

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 42.5 180 x

180 - 42.5 x 137.5 (137.5, 42.5)

x y 180 -(x - 3y 10) 4y 170

y 42.5

Using Elimination to Solve a Word Problem

The sum of two numbers is 70 and their difference

is 24. Find the two numbers.

Using Elimination to Solve a Word problem

The sum of two numbers is 70 and their difference

is 24. Find the two numbers.

x first number y second number Therefore, x

y 70

Using Elimination to Solve a Word Problem

The sum of two numbers is 70 and their difference

is 24. Find the two numbers.

x y 70

x y 24

Using Elimination to Solve a Word Problem

x y 70 x - y 24

47 y 70 y 70 47 y 23

2x 94 x 47

(47, 23)

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.