Solving Systems of Equations 2x2 Matrices

When solving a system AX=B using inverse matrices, you use the equation:

• X=A^-1B

• B=X^-1A

• A=X^-1B

• X=B^-1A

Solving Systems:
Solve for x and y
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Matrix Inverses:

• 5   -2
  -3    1

• -5   2
  3   -1

• -5   3
  2   -1

• 1   -3
  -2    5

An automobile dealership sells Model A cars and Model B trucks.  The matrix equation models a system of linear equations that relates the revenue generated from the sale of the vehicles and the number of (Model A) cars and (Model B) trucks sold in the month of April.   Which system of equations represents the matrix equation?

• a

• b

• c

• d

Solve the system by inverting the coefficient matrix and using (A^-1)(x)=b. Enter your answer as (x1, x2) format.

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Solve the matrix equation using inverse equations.

• A

• B

• C

• D

6x + y = + 5

-2x + y = 5

• (-3, -6)

• (-6, 3)

• (0, 5)

• (-3, 5)

An automobile dealership sells Model A cars and Model B trucks.  The matrix equation models a system of linear equations that relates the revenue generated from the sale of the vehicles and the number of (Model A) cars and (Model B) trucks sold in the month of April.   How many cars were sold in April?

• 8

• 10

• 18

• Impossible to know. Need more information.