# 2 Equations - Don't know where to start

• Dec 14th 2008, 12:34 PM
BackBlood
2 Equations - Don't know where to start
Ok got 2 algbaric equations.
Can someone help me here..... really really confused where to start.

Here they are...
0.8v + 0.54y -1.6z > 0

where

v + y + z = 1 (v,y or z cannot be <0)

Help much appreciated

Need value(s) for z only really, but if you can get the value(s) of y and v that would be nice too:)

I did post this in the advanced section but looking at some others this looks basic in comparison so thoguht I might get a quicker response here!

Many Thanks for your help :)
• Dec 14th 2008, 09:43 PM
earboth
Quote:

Originally Posted by BackBlood
Ok got 2 algbaric equations.
Can someone help me here..... really really confused where to start.

Here they are...
(A) 0.8v + 0.54y -1.6z > 0

where

(B) v + y + z = 1 (v,y or z cannot be <0)

Help much appreciated

Need value(s) for z only really, but if you can get the value(s) of y and v that would be nice too:)

I did post this in the advanced section but looking at some others this looks basic in comparison so thoguht I might get a quicker response here!

Many Thanks for your help :)

1. Solve (B) for \$\displaystyle v=-y-z+1\$

2. Substitute v in (A) by -y-z+1:

\$\displaystyle 0.8·(-y - z + 1) + 0.54·y - 1.6·z > 0\$

3. Solve for z:

(C) \$\displaystyle z<\dfrac{40-13y}{120}\$

4. Since all three variables have to be positive

\$\displaystyle 40-13y>0~\implies~y<\dfrac{40}{13}\$

Then
\$\displaystyle 0<z<\dfrac13\$ according to (C)

and

\$\displaystyle 0<v<\dfrac23\$ according to (B)