# basic unknowns in a system

• Dec 29th 2012, 11:57 AM
kingsolomonsgrave
basic unknowns in a system
My text says that the system

$5x+y=3$

$4x_1-x_2+3x_3=-1$

has unknowns x and y

I would have thought it has more than just x and y.

This is the full excerpt.

Attachment 26403
• Dec 29th 2012, 12:09 PM
jakncoke
Re: basic unknowns in a system
i'm pretty sure they messed up the ordering Like

(5) is supposed to be $5x+y = 3$ , $2x-y = 4$
• Dec 29th 2012, 12:24 PM
HallsofIvy
Re: basic unknowns in a system
It looks to me like they are just numbered wrong. That is "system 5" refers to the two equations on the left, 5x+ y= 3 and 2x- y=4, while "system 6" refers to the two equations on the right $4x_1- x_2+ 3x_3= -1$ and $3x_1+ x_2+ 9x_3= -4$.

The first system, two equations in two unknowns, has the unique solution x= 1, y= -2: 5(1)- 2= 3, 2(1)-(-2)= 4.

The second system, two equations in three unknowns, has an infinite number of solutions.
• Dec 29th 2012, 12:40 PM
kingsolomonsgrave
Re: basic unknowns in a system
That's what I thought might be the case. Thanks!