# Thread: basic unknowns in a system

1. ## basic unknowns in a system

My text says that the system

$\displaystyle 5x+y=3$

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

has unknowns x and y

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

This is the full excerpt.

2. ## Re: basic unknowns in a system

i'm pretty sure they messed up the ordering Like

(5) is supposed to be $\displaystyle 5x+y = 3$ , $\displaystyle 2x-y = 4$

3. ## 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 $\displaystyle 4x_1- x_2+ 3x_3= -1$ and $\displaystyle 3x_1+ x_2+ 9x_3= -4$.

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.

4. ## Re: basic unknowns in a system

That's what I thought might be the case. Thanks!