Write a system of equations with solution set {(4,5)}. |...

Name: Problem 37, Chapter 3: Intermediate Algebra
Uploaded: 2020-06-26T10:08:28-08:00
Duration: 23 s
Channel: Ankit Gupta
Description: Write a system of equations with solution set {(4,5)}.

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Key Concepts

System of Equations

A system of equations is a set of two or more equations with the same set of variables. The goal of such a system is to find values for the variables that satisfy all of the equations simultaneously. This concept is fundamental in algebra and is used to solve problems where multiple conditions must be met at the same time.

Unique Solution

A unique solution refers to a scenario in which there is exactly one set of values for the variables that satisfies all the equations in the system. In the context of a system of equations, having a unique solution means that the graphs of the equations intersect at exactly one point. This concept is important, especially when ensuring that the system is consistent and independent.

Constructing a System with a Desired Solution

When creating a system of equations with a specific solution, the equations must be carefully constructed so that the chosen solution satisfies each equation. This often involves ensuring that one equation represents a valid relationship that passes through the desired solution, and another equation is designed to intersect at that same point. Methods of eliminating or substitution are used to confirm that no other solution exists, ensuring the system is consistent and yields the unique solution.

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