Solving Systems by Elimination & Matrices

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# Solving Systems by Elimination & Matrices - PowerPoint PPT Presentation

Solving Systems by Elimination & Matrices. EQ: For what type of problems would elimination and matrices be the best method to use?. Matrices & Elimination. Works only with linear equations (no x 2 , x 3 , |x|, √x) All variables must be moved to one side. Elimination.

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## Solving Systems by Elimination & Matrices

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### Solving Systems by Elimination & Matrices

EQ: For what type of problems would elimination and matrices be the best method to use?

Matrices & Elimination
• Works only with linear equations

(no x2, x3, |x|, √x)

• All variables must be moved to one side
Elimination
• Step 1: Line up equations
• Step 2: Multiply one or both equations so that you have a pair that will cancel
• Step 3: Add equations together
• Step 4: Solve for the variable
• Step 5: Go back and find the other variable
Ex 1) Solve the system using elimination

2x – 3y = 12

4x + 3y = 6

+

6x = 18

Ex 2) Solve the system using elimination

3x – 4y = 18

3x + 9y = -7

-3x - 9y = 7

-13y = 15

Ex 3) Solve the system using elimination

3x – 2y = 8

5x + 4y=28

6x – 4y = 16

5x + 4y= 28

11x = 44

Matrix
• Row by Column

ROW

COLUMN

Reduced Row Echelen Form
• A matrix with only leading 1’s and 0’s everywhere else
Solving using “ rref ”

ax + by = c

dx + ey = f

x = r y = s

How to find RREF using Calculator:

2nd, MATRIX (x -1), EDIT, [A]

Make a 2 by 3 or 3 by 4 matrix

Enter coefficients

2nd, Quit (Mode)

2nd, x -1 → MATH, rref(

2nd, x -1 , #1 [A]

Press Enter

Solve by Matrices or Elimination

1. 5x + 2y = 8 2. 2x + y = 2

x – y = 10 -2x + 2y = 10

3. y = -2x – 4 4.

5x + 3y = -6

{

{

(-1, 4)

(4, -6)

{

(0, 2)

(-6, 8)