1. ## Rewriting an equation

I wasn't really sure where to put this problem, it is a college course but I'm having issues with the basic algebra. I figured this would be the best spot...

The textbook (macro econ) gives an equation and wants it in terms of Y, and gives the answer in two steps. I just cant figure out how the author did it.

Y=c0+c1*Y-c1*T+I+G
It then rearranges to
(1-c1)*Y=c0 +I+G-c1*T
Then it divides both sides by (1-c1) for
Y=1/(1-c1)*[c0+I+G-c1*T]

What I don't understand is where he gets the (1-c1) part. He obviously subtracted c1*Y from the right side and added it to the Y on the left hand side of the equation, but I don't know what identity he used to convert Y-c1*Y to (1-c1)*Y. Any help on clearing this up would be greatly appreciated. If any further clarification is necessary please let me know.

Clarification: The c1 and c0 are c subscript 1 and c subscript 2 (not that it really makes a difference)

2. Originally Posted by rhymenoceros
...
What I don't understand is where he gets the (1-c1) part. He obviously subtracted c1*Y from the right side and added it to the Y on the left hand side of the equation, but I don't know what identity he used to convert Y-c1*Y to (1-c1)*Y.

...
If you factor out a value from a sum you must divide each summand by the factor. The results of the division have to be written in parantheses:

Example:

$3+4+5 = 7\left(\dfrac37+\dfrac47+\dfrac57\right)$

$y-c_1 \cdot y = y\left(\dfrac yy - \dfrac{c_1 \cdot y}y \right)= y \left(1 - c_1\right)$
Maybe I should mention that $\dfrac yy = \boxed{1}$