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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 x 2 , x 3 , |x|, √x) All variables must be moved to one side. Elimination.

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solving systems by elimination matrices

Solving Systems by Elimination & Matrices

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

matrices elimination
Matrices & Elimination
  • Works only with linear equations

(no x2, x3, |x|, √x)

  • All variables must be moved to one side
elimination
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
Ex 1) Solve the system using elimination

2x – 3y = 12

4x + 3y = 6

+

6x = 18

ex 2 solve the system using elimination
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
Ex 3) Solve the system using elimination

3x – 2y = 8

5x + 4y=28

6x – 4y = 16

5x + 4y= 28

11x = 44

matrix
Matrix
  • Row by Column

ROW

COLUMN

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

ax + by = c

dx + ey = f

x = r y = s

how to find rref using calculator
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
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)