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4.4 Solving Systems with Matrix Equations4.4 Solving Systems with Matrix Equations4.4 Solving Systems with Matrix Equations4.4 Solving Systems with Matrix Equations

Objectives: •Use matrices to solve systems of linear equations in mathematical and real-world situations

Let x represent the amount invested at 4%

x + y = 5000

Example 1Amy has saved $5000 during the past three summers. Now she wants to put some of the money into an investment that earns 4% per year and some into an investment that earns 11% per year. How much money should Amy invest at each interest rate to earn $500 in interest per year?

Step 1: Choose your variables

Let y represent the amount invested at 11%

Step 2: Write a system of equations

.04x + .11y = 500

Step 3: Write the system as a matrix equation, AX = B

1 1

.04 .11

x

y

5000

500

Step 4: Solve for the variable matrix, X, by finding the product A-1B

$714.29 at 4% and $4285.71 at 11%

Example 2Refer to the system of equations below.

a) Write the system as a matrix equation

b) Solve the matrix equation

3x 6y 4z 8

x 4y 2z 3

8y z 0

3 6 4

1 4 2

0 8 1

x

y

z

8

3

0

13 6 4

1 4 2

0 8 1

x

y

z

8

3

0

1.8

0.1

0.8

x = - 1.8 y = - 0.1 z = - 0.8

Example 3Refer to the system of equations below.

a) Write the system as a matrix equation

b) Solve the matrix equation

9x 3y 27

6x 2y 18

9 3

6 2

x

y

27

18

19 3

6 2

x

y

27

18

PracticeRefer to the system of equations below.

a) Write the system as a matrix equation

b) Solve the matrix equation

3x 4y 3

6x 8y 6

Homework

Worksheet