Transcript Solve the system using inverse matrices

Solving Systems
Using Inverse Matrices
Solve the system
using inverse matrices
3x + 2y = 7
4x - 5y = 11
You can use the inverse
of the coefficient matrix
to find the solution.
3 2 
4  5


Set up a matrix equation
to find the solution.
3 2 
4  5


 x  7 
 y   11
   
The formula to find the
solution is:
1
A B
 
  
 
57
23
5
23
solution 
5723 , 235 
Solve the system
using inverse matrices
2x - 4y = 9
3x - 2y = 1
 2  4
 3  2


Set up a matrix equation
to find the solution.
2  4  x  9
3  2  y   1

   
The formula to find the
solution is:
1
A B
 
  
 
7
4
 25
8
solution 
 47 , 825 
Solve the system
using inverse matrices
x + 4y = 8
2x - 2y = -6
1 4 
 2  2


Set up a matrix equation
to find the solution.
1 4 
 2  2


 x  8 
 y     6
   
The formula to find the
solution is:
1
A B
 
  
 
4
5
11
5
solution 
 54 , 115 
Solve the system
using inverse matrices
2x  3y  z  2
x  2y  z  3
 x  y  3z  1
 2 3  1
A   1 2 1 
 1  1 3 
Set up a matrix equation
to find the solution.
 2 3  1  x  2
 1 2 1   y    3

   
 1  1 3   z  1 
The formula to find the
solution is:
1
A B
 5
  4 
 0 
solution   5,4,0 
Practice:
 Page 45 #1-10
 worksheet