# Changing the subject of the formulae

• Sep 20th 2012, 11:51 AM
joe345
Changing the subject of the formulae
Please may someone show me the steps to changing the subject for the following questions, the subject needs to be y for each one.

1) h-y
h+y = k

2) y+3 d
y-2 = e
• Sep 20th 2012, 11:52 AM
joe345
Re: Changing the subject of the formulae
Sorry everything has been moved to the left a little.
• Sep 20th 2012, 12:41 PM
Soroban
Re: Changing the subject of the formulae
Hello, joe345!

Quote:

$\text{(1) Solve for }y\!:\;\frac{h-y}{h+y} \:=\:k$

Multiply by $(h+y)\!:\;h-y \:=\:k(h+y)$

Expand: . . . . . . . . $h-y \:=\: kh + ky$

Get all y-terms to one side:

. . . . . . . . . . . $\text{-}ky - y \:=\:kh - h$

Factor: . . . . $\text{-}(k+1)y \:=\:h(k-1)$

Divide by $\text{-}(k+1)\!:\;\:y \:=\:\frac{h(k-1)}{\text{-}(k+1)}$

Multiply by $\tfrac{\text{-}1}{\text{-}1}\!:\qquad\; y \:=\:\frac{h(1-k)}{1+k}$

[The last step is not necessary, but the answer is neater.]

Quote:

$\text{(2) Solve for }y\!:\;\frac{y+3}{y-2} \:=\:\frac{d}{e}$

Cross-multiply: . $e(y+3) \:=\:d)y-2)$

Expand: . . . . . . $ey + 3e \:=\:dy - 2d$

Get y-terms on one side:

. . . . . . . . . $ey - dy \:=\:\text{-}3e -2d$

Factor: . . . $(e-d)y \:=\:\text{-}(3e+2d)$

Divide by $(e-d)\!:\; y \:=\:\frac{\text{-}(3e+2d)}{e-d}$

Multiply by $\tfrac{-1}{-1}\!:\quad\; y \:=\:\frac{2d+3e}{d-e}$
• Sep 20th 2012, 12:49 PM
joe345
Re: Changing the subject of the formulae
Thankyou very much