Unsure of how to solve a certain set of simultaneous equations

[azorbz]

Last week I was searching online for some practice questions, and I came across this question which I couldn't solve. I've been trying for the past week, but just don't know how.

The question:

The two equations are the same, but visually flipped 180 degrees.

((x-1)/9) - (6/z) = 1

(z/9) - (6/(1-x)) = 1

 

[tkhunny]

1) How would you normally go about such a thing?
2) How is this any different?

We know x is not 1 and z is not 0 (How?).

Give this a try?

z(x-1) - 54 = 9z
z(1-x) - 54 = 9(1-x)

How did I get that? Is that better or worse?

What if we wrote it this way?

z(x-1) - 54 = 9z
z(x-1) + 54 = 9(x-1)

Where did that come from? What's stopping you from solving either equation for either x or z?

If you show your work in the very first post, you can get more specific help much more quickly. After a week-long struggle, surely you have something.

 

[Deleted member 4993]

Last week I was searching online for some practice questions, and I came across this question which I couldn't solve. I've been trying for the past week, but just don't know how.

The question:

The two equations are the same, but visually flipped 180 degrees.

((x-1)/9) - (6/z) = 1

(z/9) - (6/(1-x)) = 1

I would substitute:

u = x - 1

Then

u/9 - 6/z = 1...........................(1)
z/9 + 6/u = 1...........................(2)

so we have:

uz - 54 = 9z...........................(3)
uz + 54 = 9u...........................(4)

we get

2uz = 9(u+z)...........................(5)
108 = 9(u-z)...........................(6)

Here we have \(\displaystyle u \ \ne \ \ 0 \ and \ z \ \ne \ \ 0\)

and continue
Not any easier to solve - just looks easier....