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Chapter 5: Problem 69

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I use the same steps to solve nonlinear systems as I did to solve linear systems, although I don't obtain linear equations when a variable is eliminated.

Short Answer

Expert verified
The statement is partially correct. While some strategies used in solving linear systems can also be used in nonlinear ones, the resulting equations when a variable is removed in nonlinear systems aren't always linear.

Step by step solution

01

Understanding Linear and Nonlinear Systems

Linear and nonlinear systems differ in the equations they consist of; linear systems are comprised of linear equations, while nonlinear systems consist of at least one nonlinear equation. This fundamental difference often leads to different solving methods.
02

Solving Linear and Nonlinear Systems

While some steps may be shared between solving linear and nonlinear systems (like substitution or elimination), one should note that the behavior of these two systems differs greatly. In nonlinear systems, removing a variable doesn't necessarily result in a linear equation, whereas in linear systems, it does.
03

Conclusion

The statement is partially correct, some similar steps might be applied when solving both types of systems, but the outcome won't always be a linear equation when a variable is eliminated in a nonlinear system. So, care must be taken when handling nonlinear systems to avoid incorrect conclusions.

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Most popular questions from this chapter

In Exercises 106-109, determine whether each statement makes sense or does not make sense, and explain your reasoning. When graphing \(3 x-4 y<12,\) it's not necessary for me to graph the linear equation \(3 x-4 y-12\) because the inequality contains a \(<\) symbol, in which equality is not included.

Use the two steps for solving a linear programming problem, given in the box on page 577 , to solve the problems in Exercises 17鈥�23. A manufacturer produces two models of mountain bicycles. The times (in hours) required for assembling and painting each model are given in the following table: $$\begin{array}{lcc}\hline & \text { Model } A & \text { Model } B \\\\\hline \text { Assembling } & 5 & 4 \\\\\text { Painting } & 2 & 3\end{array}$$ The maximum total weekly hours available in the assembly department and the paint department are 200 hours and 108 hours, respectively. The profits per unit are \(25 for model A and \)15 for model B. How many of each type should be produced to maximize profit?

Explain how to solve a nonlinear system using the addition method. Use \(x^{2}-y^{2}-5\) and \(3 x^{2}-2 y^{2}-19\) to illustrate your explanation.

The group should write four different word problems that can be solved using a system of linear equations in two variables. All of the problems should be on different topics. The group should turn in the four problems and their algebraic solutions.

Write a system of equations having \([(-2,7)]\) as a solution set. (More than one system is possible.)
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