# Making Y the subject of equations:i) c=3m/2m+y ii) xy/x+y = k.I'm having trouble isolating the y pronumeral for both equations, so if you could show it step by step for the solution, that'd be...

Making Y the subject of equations:i) c=3m/2m+y ii) xy/x+y = k.

I'm having trouble isolating the y pronumeral for both equations, so if you could show it step by step for the solution, that'd be great thanks :D

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### 3 Answers

I see you already have two answers, but I thought I would give it a go anyways ;)

i) c=3m/(2m+y)

The first step is to get y in the numerator instead of the denominator. We can do this by multiplying both sides by (2m+y):

(2m+y)c = 3m(2m+y)/(2m+y)

On the right hand side of the equation you can solve (2m+y)/(2m+y) = 1 to give:

(2m+y)c = 3m

Next you want to get y out of the brackets. To do this multiply c into the brackets:

2mc + yc = 3m

Now we can begin to isolate y. Mvoing 2mc to the right hand side of the equation changes its sign to negative:

yc = 3m - 2mc

Now we can divide both sides the the equation by c, and eliminate c/c = 1 on the left hand side of the equation:

y = (3m - 2mc)/c

In the above equation m can be factored out to give the final answer:

**y = m(3 - 2c)/c**

ii) xy/(x+y) = k

On first glance this one looks more complicated, but lets follow a similar method as in i) and see what happens. First, get rid of the denominator by multiplying both sides by (x+y):

xy = (x+y)k

Next, expand the right hand side of the equation:

xy = kx+ky

Group all variables containing the unknown y:

xy-ky = kx

Factor out y:

y(x-k) = kx

And finally, isolate y:

**y = kx / (x-k)**

When you are approached with questions like this just remember, elimate fractions, expand, isolate, factor if necessary ;)

c = 3m/(2m + y)

First let us cross multiply:

==> c(2m + y) = 3m

Open brackets:

==> 2cm + cy = 3m

==> cy = 3m -2cm

**==> y = m(3-2c)/c**

** **

2) k = xy/(x+y)

Cross multiply:

==> k(x+ y) = xy

==> kx + ky = xy

==> ky - xy = -kx

==> y (k-x) = -kx

==> **y = -kx/(k-x)**

Making y subject is as good as solving for y from the same formula treating other varibles as known.

i) c=3m/2m+y ii) xy/x+y = k

Solution:

c = 3m/(2m+y) , Multiply by 2m+y

c(2m+y) =3m

2mc+cy =3m

cy = 3m-2mc

y = (3m-2mc)/c

y = m(3-2c)/c

ii)

xy/(x+y) = k. Multiply by (x+y) Proceed to solve for y treating the others as known. So,

xy = k(x+y)

xy =x+ky

xy - ky = x

(x-k)y = x

y = x/(x-k)