Chapter Outline
In this unit, you’ll discover how systems of equations are incredibly useful in the real world by allowing us to model and solve problems involving multiple variables and constraints. For instance, in business and economics, systems of equations help model supply and demand, optimize production schedules, and manage resources efficiently. This means businesses can determine the best combination of products to maximize profit while considering constraints like budget and labor. Engineers rely on systems of equations to analyze and design complex systems, such as electrical circuits, structural frameworks, and fluid dynamics, ensuring these systems function correctly under various conditions. In science and medicine, systems of equations model biological processes, chemical reactions, and population dynamics, providing insights that can lead to new discoveries and treatments. Through this unit, you will learn how to apply these powerful mathematical tools to solve real-world problems effectively.​
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2.1
Exploring Systems of Linear Equations
Learning Objectives
By the end of this section, you will be able to:
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Identify the solution of a system of two linear equations from a graph
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Verify the solution of a system of equations algebraically
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Determine if a point is a solution to a system of two linear equations
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Analyze and solve real-world problems using systems of linear equations
2.2
Solving Systems - Graphing
Learning Objectives
By the end of this section, you will be able to:
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Solve a system of linear equations by graphing
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Determine when a linear system will have one solution no solution or infinitely many solutions
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Use technology to find exact and approximate solutions to a system of linear equations
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Verify the solution to a system of linear equations algebraically
2.3
Solving Systems - Substitution
Learning Objectives
By the end of this section, you will be able to:
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Create a system of linear equations from a graph or table in slope-intercept form
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Isolate a variable in one of the equations of a linear system
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Solve a system of linear equations using substitution
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Verify the solution to a system of equations by substituting the values back into the original equations
2.4
Introduction to Linear Combinations
Learning Objectives
By the end of this section, you will be able to:
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Interpret the solution in the context of the problem
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Model problems using a system of linear equations
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Create equivalent linear equations by multiplying by a constant
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Solve systems of two linear equations using the linear combination method
2.5
Linear Combinations
Learning Objectives
By the end of this section, you will be able to:
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Model problems using a system of linear equations
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Create equivalent linear equations by multiplying by a constant
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Interpret the solution in the context of the problem
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Solve systems of two linear equations using the linear combination method
2.6
Solving Systems of Inequalities
Learning Objectives
By the end of this section, you will be able to:
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Graph systems of linear inequalities
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Identify solution sets of systems of linear inequalities
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Analyze the solution sets of systems of linear inequalities
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Determine whether a point satisfies a system of linear inequalities