Mathematics for Technology II (Math 2131)

Durham College, Mathematics
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• 0 lessons
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• 14 week duration
• Solving Systems of Equations

This unit introduces how to systematically solve a system of equations, namely linear equations. Examples of non-linear systems, including systems of 3 unknowns will be of emphasis.

• Graphs of Trigonometric Functions

The unit focuses primarily on how to graph periodic sinusoidal functions, and how to identify features of a waveform to produce an equation by inspection.

• Polar Coordinate Functions

An introduction to the polar coordinate system.

• Complex Numbers

This unit is an extension of what was introduced in Math 1131. To learn how to work with radicals, knowing your exponent laws in crucial. Hence, this unit begins with a thorough review.

• Logarithmic Functions

This chapter introduces you to exponential functions, and how they can be solved using logarithms.

• Trigonometric Identities and Equations
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• Analytic Geometry
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Mathematics for Technology II (Math 2131)

Introduction

This chapter introduces us to solving a system of equations. In part one of this course (Math 1131), you learned how to solve linear equations (such as, 25 = x + 5), for the unknown variables. This time you’ll learn to solve a system of linear equations with two unknowns, such as:

$–2x+1=y\phantom{\rule{0ex}{0ex}}x=3–y\phantom{\rule{0ex}{0ex}}$

The reason this is important is because systems of equations appear in almost every branch of science and engineering. Some problems in technology can only be described by two equations. For example, to find the two currents I1 and I2 in the circuit below, you must solve the two equations simultaneously:

 $98.0{I}_{1}–43.0{I}_{2}=5.00\phantom{\rule{0ex}{0ex}}–43.0{I}_{1}+115.0{I}_{2}=10.0\phantom{\rule{0ex}{0ex}}$

In this problem, we have two unknowns (I1 and I2, rather than the typical x and y) found in two separate linear equations. We know they’re both linear equations because both variables are of first degree (having an exponent of 1). We must find values for I1 and I2 that satisfy both equations at the same time. The answer to this problem will be revisited at a later section. Just as some applications need two equations for their description, others need three equations – we also study those in a later section.

What’s interesting about the techniques you will learn in this chapter is that they can be applied to a system of any two questions, that is, the equations don’t have to be linear. Of course, they’re relatively easier to solve if they are of first degree. Many textbooks refer to solving systems of equations as solving simultaneously.

To solve a system of two linear equations means to find the point of intersection when both are graphed on an x-y plane. In other words, by solving a system of two linear equations, you are finding out the coordinates where the two lines intersect. The first technique to solving is by graphing the equations manually, then reading the point where the two lines intersect.

Question:   Find the solution to the following system by graphing.

$2x+y=–1\phantom{\rule{0ex}{0ex}}x–y=–5\phantom{\rule{0ex}{0ex}}$

Solution: Assuming you already learned how to graph linear equations without a table (see link).