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Chapter 4: Problem 58

What is an inconsistent system? What happens if you attempt to solve such a system by graphing?

Short Answer

Expert verified
An inconsistent system is a system of equations or inequalities that has no solution. In a graphical representation, the lines or curves for the individual equations will never intersect indicating no common solution.

Step by step solution

01

Understanding Inconsistent Systems

Inconsistent system in mathematics refers to a system of equations or inequalities that has no solution. This simply means, no matter which method is used to solve the system, you will always find that there is no possible set of values that can satisfy all the equations or inequalities in the system at once. In simpler terms, none of the possible solutions of one equation are solutions of the other equation(s).
02

Graphical Representation of Inconsistent System

If you try to solve or represent such an inconsistent system graphically, you will find that the lines (in a system of linear equations for instance) or curves (for non-linear systems) of the individual equations or inequalities will never intersect, or for some systems, they may be parallel. Remember, the points of intersections are the solutions in a graphical representation. Therefore, no intersection means no common solution.

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Most popular questions from this chapter

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}2 x-3 y=10 \\ 4 x+3 y=20\end{array}\right.$$

In Exercises \(45-56,\) solve each system by the method of your choice. If there is no solution or an infinite number of solutions, so state. Use set notation to express solution sets. Explain why you selected one method over the other two. $$\left\\{\begin{aligned} 3 x-2 y &=8 \\ x &=-2 y \end{aligned}\right.$$

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}y=2 x+2 \\ y=-2 x+6\end{array}\right.$$

Read Exercise \(72 .\) Then use a graphing utility to solve the systems. $$\left\\{\begin{array}{l}y=-\frac{1}{2} x+2 \\ y=\frac{3}{4} x+7\end{array}\right.$$

When using substitution to solve $$\left\\{\begin{array}{rr}5 x-4 y= & 9 \\\x-2 y= & -3\end{array}\right.$$ I find it easiest to solve for \(x\) in the first equation.
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