Help with some basic simplification and distribution

[minister1221]

Hi everyone,

I'm extremely rusty with any math as it has been over a decade since I've studied it.
Could someone please walk me through what is happening with these line by line? I can't follow the equation flow and see why the ending result for x and y are what they are.

-xs + 1 - x = 1/2
x(1 + s) = 3/2
x = 3/(2 + 2s)

===========

(s)(y - 2x)/y = -1
sy - 2sx = -y
s - s2x/y = -1

y = s2x/(s + 1)

From earlier, x = 3/(2 + 2s)
Substitute for x:
y = 3s/(1+s)^2



Thanks in advance.

 

[JeffM]

One reason that you cannot follow the first one is because it is wrong.

[MATH]-xs + 1 - x = \dfrac{1}{2} \implies[/MATH]
[MATH](-2)(- xs + 1 - x) = (-2) * \dfrac{1}{2} \implies[/MATH]
[MATH]2xs - 2 + 2x = - 1 \implies[/MATH]
[MATH]2 + 2xs - 2 + 2x = 2 - 1 \implies[/MATH]
[MATH]2 - 2 + 2xs + 2x = 1 \implies[/MATH]
[MATH]2xs + 2x = 1 \implies[/MATH]
[MATH]x(2s + 2) = 1 \implies[/MATH]
[MATH]\dfrac{1}{2s + 2} * x(2s + 2) = \dfrac{1}{2s + 2} * 1[/MATH]
[MATH]x = \dfrac{1}{2s + 2}.[/MATH]
Of course you may have changed a minus 1 to a plus 1 in the initial equation.

The second one is correct, but it is a convoluted approach.

[MATH]s(y - 2x)/y = - 1 \implies[/MATH]
[MATH]s(y - 2x) = - y \implies[/MATH]
[MATH]sy - 2sx = - y \implies[/MATH]
[MATH]sy + y = 2sx \implies[/MATH]
[MATH]y(s + 1) = 2s * x \implies[/MATH]
[MATH]y = \dfrac{2s}{s + 1} * x.[/MATH]

 

[minister1221]

It looks like I made a typo with the first half.
It should be negative one-half and not positive one-half.

-xs + 1 - x = -1/2

Thank you so much for the help on the second half and I will be reviewing it.