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5 – Systems of Linear Equations

• There’s a deafening roar as an airplane races down the runway, gains speed, and takes off into the sky.
• Flying against the wind, it will cover a thousand miles in two hours. On its return trip, in calm air, it will cover the same distance in half the time.
• With this information, could you determine the velocity of the wind during the first leg? Could you calculate the plane’s speed when there’s no wind? Airlines and air traffic controllers can.
• You could too, using a system of linear equations. Did you know that all sorts of real-world problems are can be solved using a system of two equations? Systems of equations are usually two equations that have the same two variables. Here are two examples.
• Imagine you’re captain of a rowing team. To prepare for the big race, your crew rows fourteen miles downstream and back in five hours.
• What additional information would allow you to calculate your team’s rowing speed? Did you guess “the speed of the river’s current?”
• In this unit, you will build on the knowledge you previously learned and discover a variety of methods for solving systems of linear equations and inequalities.

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