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# Why It Matters

## Solve systems of linear equations using matrices and solve problems in manufacturing and investment

### Introduction

You sit down with your bookkeeper to go over some bills, which are vague. Company Q simply sends you the total of items ordered and the total cost. It does not give you a price breakdown. It is midnight, and you have a report due the next morning which requires you to give the prices you are currently paying for products x, y, and z. How do you determine this?
 Quantity for x Quantity for y Quantity for z Total on bill before taxes Invoice 1 1 5 6 1400 Invoice 2 2 4 8 1400 Invoice 3 4 3 12 1600
100, 200, 50

### Learning Outcomes

• Construct linear systems of equations to model business situations
• Perform basic matrix operations, including adding, subtracting, and multiplying matrices
• Use row reduction of matrices to solve a linear system of equations
• Find the inverse of a matrix (including bigger than 2x2)
• Use the matrix inverse to solve a system of linear equations
• Solve business applications of linear systems, including some with 3 or more variables.