Inverses 2

Example: Solve the system of equations using a matrix equation.
3x + 4y = 15
-2x + 5y = 13

System of equations written as a matrix multiplication equation

multiply both sides by inverse matrix

the 2x2 matrix and its inverse cancel on the left

replace inverse matrix by defininition

finding the determinant

simplifying denominator

simplifying denominator

matrix multiplication

simplify

simplify

scalar multiplication

Solving Equations with Matrices Practice: Solving a system of equations using matrix equations.

#1)  5x + 3y = -31
       4x + 2y = -22


#2)  7x + 4y = -17
       8x + 5y = -19

Homework

Solving Equations with Matrices

Solve each system of equations by using matrix equations.
#1) 5x + y = 26
      2x - 3y = 41

#2) 5x + y = 1
      9x + 3y = 1

#3) x + 4y = 12
      3x - 2y = -6

#4) x + y = -2
      3x - y = 10

#5) 3x - 2y = -6
       x + y = -2

#6) 3x - y = 10
       x + 4y = 12

Answers Solving Equations with Matrices

#1) (7, -9)
#2) (1/3, -2/3)
#3) (0, 3)
#4) (2, -4)
#5) (-2, 0)
#6) (4, 2)