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3-2: Solving Systems of Equations using Elimination

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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 ... – PowerPoint PPT presentation

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Title: 3-2: Solving Systems of Equations using Elimination


1
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.
2
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
3

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).
4
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
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.
6
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
7

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).
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
9
NOW solve these using elimination
1.
2.
2x 4y 1 x - 4y 5
2x y 6 x y 3
10
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.
11
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
12
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
13
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
14
Using Elimination to Solve a Word Problem
The sum of two numbers is 70 and their difference
is 24. Find the two numbers.
15
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
16
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
17
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)
18
Now you Try to Solve These Problems Using
Elimination.
Solve
  1. Find two numbers whose sum is 18 and whose
    difference is 22.
  1. The sum of two numbers is 128 and their
    difference is 114. Find the numbers.
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