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Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

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May 9th, 2018, 03:20 AM   #1
Joined: Apr 2018
From: Banovo Brdo

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System of equations

Subtracting 1st from 2nd, and 2nd from 3rd:
&\implies z-y=y-x\Leftrightarrow z=2y-x
How do I proceed from here? I've been at it for quite a while, and I still feel like I'm just short of untangling it. Thanks.
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May 9th, 2018, 03:44 AM   #2
Joined: Jan 2018
From: Belgrade

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Try to do this:

$\displaystyle (y-x) \cdot 3y=3$, that is:

$\displaystyle (y-x) \cdot y=1$.

From here: $\displaystyle x=y-\frac{1}{y}$.

Put it in the first equation, and you get:

$\displaystyle 3y^{2}+\frac{1}{y^{2}}=4$

Substitute $\displaystyle t=y^{2}$ and you have:

$\displaystyle 3t^{2}-4t+1=0$
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