There is another way of telling whether a system of two linear equations in two unknowns is consistent or inconsistent, or whether the equations are dependent, without taking the time to graph each equation. It can be shown that any system of the forma1x + b1y = c1a2x + b2 y = c2has one and only one solution ifa1/a2 ≠ b1/b2 that it has no solution ifa1/a2 = b1/b2 ≠ c1/c2 and that it has infinitely many solutions ifa1/a2 = b1/b2 = c1/c2For each of the following systems, determine whether the system is consistent, the system is inconsistent, or the equations are dependent. x - 3y = 5 3x - 9y = 15

Given, x-3y=5 .......13x-9y=15 .......2

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College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter5: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 4CC

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There is another way of telling whether a system of two linear equations in two unknowns is consistent or inconsistent, or whether the equations are dependent, without taking the time to graph each equation. It can be shown that any system of the form
a₁x + b₁y = c₁
a₂x + b₂ y = c₂
has one and only one solution if
a₁/a₂ ≠ b₁/b₂ that it has no solution if
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ and that it has infinitely many solutions if
a₁/a₂ = b₁/b₂ = c₁/c₂
For each of the following systems, determine whether the system is consistent, the system is inconsistent, or the equations are dependent. x - 3y = 5
3x - 9y = 15

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