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DiscussionMake up a system of three linear equations in three variables for which the solution set is $\{(0,0,0)\} .$ A system with this solution set is called a homogeneous system. Why do you think it is given that name?

because constant term of each equation is zero.

Algebra

Algebra 2

Chapter 4

Systems of Linear Equations

Section 3

Systems of Linear Equations in Three Variables

Polynomials

Systems of Equations and Inequalities

Introduction to Algebra

Graph Linear Functions

Write Linear Equations

Linear Equations and Functions

Matrices and Determinants

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right. So this problem we asked to make a system of three linear equations and three variables sports. The solution said 000 To do this, we can just notice that if we set the right side of these equations equals zero, then we're gonna have If I was, like ax plus, uh, two y plus three z here, and we have negative X plus five y minus 70 here. When you have, you know, negative four acts plus two y minus Z equals here. Here, +000 is the solution. Uh, we don't worry about eliminating or substituting any system of three variables with three equations where the right side include zero. You're gonna be able to plug in zero for X Y and Z gets here. So this is called that tells a homogeneous system. Why do you think it's given this name? Because you can multiply these numbers by any value. They're still gonna have 000 as a solution

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