Solve the folowing system of equations

$\begin{cases}

& \text{ if } {x}^{3}(1-x)+{y}^{3}(1-y) =12xy+18\\

& \text{ if } |3x-2y+10|+|2x-3y|=10

\end{cases}$ (Không nói nên lời)

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- May 20th 2013, 01:21 AMthth776Solve the folowing system of equations
Solve the folowing system of equations

$\begin{cases}

& \text{ if } {x}^{3}(1-x)+{y}^{3}(1-y) =12xy+18\\

& \text{ if } |3x-2y+10|+|2x-3y|=10

\end{cases}$ (Không nói nên lời) - May 20th 2013, 12:23 PMDavidBRe: Solve the folowing system of equations
Your post is not displaying correctly (at least for me).

What kind of code is that?

Is that supposed to be LaTeX? - May 25th 2013, 01:35 AMEducatedRe: Solve the folowing system of equations
Is it supposed to be like this?

Quote:

Solve the folowing system of equations

$\displaystyle \begin{cases} \text{ if } {x}^{3}(1-x)+{y}^{3}(1-y) =12xy+18\\ \text{ if } |3x-2y+10|+|2x-3y|=10 \end{cases}$

- May 26th 2013, 03:57 AMthth776Re: Solve the folowing system of equations
- May 26th 2013, 06:07 AMHallsofIvyRe: Solve the folowing system of equations
Help you how? We have no idea what you know or can do with this, and so can not give any hints, since you have shown no work of your own.

- May 27th 2013, 03:03 AMthth776Re: Solve the folowing system of equations
- May 27th 2013, 04:37 AMtopsquarkRe: Solve the folowing system of equations
See the original thread here.

We are not a homework service. We are here to help, not solve your problems for you. And multiple postings isn't going to solve your problem for you.

-Dan - May 27th 2013, 06:17 PMthth776Re: Solve the folowing system of equations
- May 28th 2013, 04:36 AMtopsquarkRe: Solve the folowing system of equations
thth776 is taking a vacation.

Still, if anyone knows how to start this I'd appreciate the hint. I'm kinda curious how to go about this one myself.

-Dan

Edit: Silly me. Just graph the thing. No worries then. - May 31st 2013, 07:21 PMibduttRe: Solve the folowing system of equations
There could be a different approach. Let us see if get a different idea. In the mean time have this

Hint: recollect the definition of modulus function, |x| = x for all x >= 0 and |x| = -x for all x <0.

For second case first go by the assumption that 3x-2y+10 >0 and 2x-3y>0, then proceed by solving with elimination by substitution. - May 31st 2013, 07:41 PMLambinRe: Solve the folowing system of equations
In other words, because 3x-2y+10 and 2x-3y are expressed as absolute-value functions, we have to assume both for when they are positive, and for when they are negative.

Because the two absolute value functions are being added together, they are commutative, and four possibilities will arise. Two of which will have real-valued solutions.

One of them is easy enough to solve.

The other requires solving a quartic function. - Jun 4th 2013, 05:27 AMthth776Re: Solve the folowing system of equations
- Jun 4th 2013, 01:17 PMLambinRe: Solve the folowing system of equations
Sure. When you think about absolute value functions, by definition, we know that the outcome is always positive no matter whether we have a negative or positive value on the inside.

For example,

|3| = 3 and |-3| = 3.

*It didn't matter whether it was a 3 or a -3, the outcome is a positive 3.*

So, if we turned things around and wanted to solve for an unknown variable in an absolute value function:

|x| = ?

How would we know whether the x was a positive or negative value? Regardless of whether it is positive or negative, the outcome is going to be the same—it will be a positive outcome.**So because they share the same outcome, we consider both the positive and negative value as solutions of the absolute-value function that are both valid.**In this latter example, it would mean that we have to consider BOTH x and -x as solutions.

How does this connect with our problem in this post?

When we work with analytic expressions instead of numbers in absolute-value functions, we don't treat them differently.

So, with $\displaystyle |4x+3|=y$, we have to consider two things:

1. $\displaystyle 4x+3=y$

2. $\displaystyle -(4x+3)=y$

See?

This would mean that for $\displaystyle |3x-2y+10|+|2x-3y|=10$, you would discover that there would be four equations. Think about what was shown earlier, and see how it relates with this problem. With these four equations, we have a system of equations with $\displaystyle x^3(1-y)+y^3(1-x)=12xy+18$.

You would have to solve from here—seeing where the four equations intersect with $\displaystyle x^3(1-y)+y^3(1-x)=12xy+18$. - Jun 5th 2013, 05:00 AMthth776Re: Solve the folowing system of equations
- Jun 30th 2013, 07:21 PMthth776Re: Solve the folowing system of equations
Toàn là một lũ cùi mía, đ' đứa nào bít giải, dẹp mẹ cái trang này đi