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Chapter 7: Problem 93

What is a system of linear equations? Provide an example with your description.

Short Answer

Expert verified
A system of linear equations is a set of two or more linear equations that involve the same set of variables. For instance, the equations \[2x - 3y = 8\] and \[x + 4y = -2\] form a system of linear equations.

Step by step solution

01

Definition of System of Linear Equations

A system of linear equations is a set of two or more linear equations involving the same set of variables.
02

Explain the Components of a Linear Equation

A linear equation is one where all variables appear to the power of one and are not multiplied together. Each linear equation represents a straight line when graphed, and the system of linear equations represents the points where these lines intersect.
03

Provide an Example

For example consider these two equations: \[2x - 3y = 8\] and \[x + 4y = -2\] These equations form a system of linear equations. We can find the solution by methods such as substitution or elimination.

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Most popular questions from this chapter

Graphing utilities can be used to shade regions in the rectangular coordinate system, thereby graphing an inequality in two variables. Read the section of the user's manual for your graphing utility that describes how to shade a region. Then use your graphing utility to graph the inequalities. $$y \leq 4 x+4$$

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