This tag indicates that several equations (of some type) must all hold. Do not use alone! Use in conjunction with (linear-algebra), (polynomials), (pde), (differential-equations), (inequalities) or another tag that describes the nature of the equations being considered.

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1
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0answers
21 views

How to properly detect rows to be swapped in a Gaussian elimination?

I'm trying to describe an algorithm for solving solvable linear systems. The Gaussian elimination is pretty straightforward in terms of adding multiples of rows. However, consider the following ...
2
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1answer
26 views

Name and explanation of a Numerical Analysis method for solving systems of non-linear equations

In a non-english textbook of Numerical Analysis there is a method for solving systems of non-linear equations. But not only I can't understand how this method is used but I can't even found the name ...
1
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1answer
44 views

solve system equation: $ a \cdot b = 3 \cdot a-b+1, b \cdot c = 3 \cdot b - c + 1, c \cdot a = 3 \cdot c - a + 1$

I want to solve this system of equations but i'm stuck. Here is it: $$ a \cdot b = 3 \cdot a - b + 1 $$ $$ b \cdot c = 3 \cdot b - c + 1 $$ $$ c \cdot a = 3 \cdot c - a + 1 $$
1
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2answers
18 views

System of non-homegeneous linear equations

I need to find a relation between $a$, $b$, $c$, $d$ in order the system with the following augmented matrix has at least one non-trivial solution. I have tried both the Gaussian and Gauss-Jordan ...
0
votes
2answers
84 views

Find x, if $ \log _{15}\left(\frac{2}{9}\right)^{\:}=\log _3\left(x\right)=\log _5\left(1-x\right) $

So how can I find the value of x, if: $$ \log _{15}\left(\frac{2}{9}\right)^{\:}=\log _3\left(x\right)=\log _5\left(1-x\right) $$ I tried switching everything to base 15, but that didn't work out ...
0
votes
1answer
24 views

Solve the system of equations by variable estimation

Solve the system of equations: $\left\{\begin{array}{l}(x-1)\sqrt{x-y^2}=y(x-2y+1)\\y\sqrt{x-1}+3\sqrt{x-y^2}=2x+y-1\end{array}\right.$ I guess there is only one solution $(x;y)=(2;1)$. This is my ...
0
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2answers
45 views

Convergence of a particular fixed point iteration scheme

Setup I have the following non-linear system of equations: $$ \mathbf{x} P(\mathbf{x}) = 0 $$ where $\mathbf{x} \in \mathbb{R}_{>0}^n$ is a probability distribution, i.e., $\sum_i x_i = 1$, and ...
0
votes
1answer
35 views

Solve the system of equations with one symmetrical equation

Solve the system of equations: $\left\{\begin{array}{l}x^3-y^3+(3x^2+y-2)\sqrt{y+1}-(3y^2+x-2)\sqrt{x+1}=0\\x^2+y^2+xy-7x-6y+14=0\end{array}\right.$ I used wolframalpha.com and got the solution: ...
5
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0answers
47 views

Solve the system of equations with $x=y$

Solve the system of equations: $\left\{\begin{array}{l}\sqrt{x^2+(y-2)(x-y)}+\sqrt{xy}=2y\\\sqrt{xy+x+5}-\dfrac{6x-5}{4}=\dfrac{1}{4}\left(\sqrt{2y+1}-2\right)^2\end{array}\right.$ I used ...
0
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1answer
29 views

How to find the position on a circle that satisfies two constraints?

Say I'm given an point P1 at coordinates $(x_1,y_1)$, and another point $P_2$ at coordinates $(x_2,y_2)$. Then I have a point $P_0$ that needs to be at coordinates $(x,y)$ such that it is a fixed ...
2
votes
2answers
46 views

Solve the follwing system of equations for $x, y$ and $z$

$$\frac{y+z}{5}=\frac{z+x}{8}=\frac{x+y}{9}$$ and $$6(x+y+z)=11$$ My teacher told me that I would have to get $3$ different equations to get $x, y$ and $z$. I've tried many methods and I'm confused ...
0
votes
0answers
32 views

When is this iteration guaranteed to converge

I have a nonlinear $N$-component equation of the form $x_n = \sum_m f_n(x_m),$ where $f$ is some function and the goal is to find a set of $x_n$ that satisfies this equation. I have experimented ...
1
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0answers
25 views

Lagrange multipliers, once I use the constraint equation, do I have to worry about it again later?

I am solving $ grad [f(x,y,z)]$ = $\lambda$grad[g(x,y,z)] I have then three equations, one involving x's and lambdas, another involving y's and lambdas and a third involving z's and lambdas. I then ...
1
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5answers
138 views

I need Integer Solution to this Equation [duplicate]

I need to know how to solve this equation where x and y are both variables Find integer Solutions. $$ \frac{1}{x} + \frac{1}{y} = \frac{1}{2} $$ from what I know I need at least 2 equations to solve ...
3
votes
2answers
237 views

How exactly do we do Gauss elimination?

This is a matrix: $$\begin{bmatrix} 1 & 1 & 1\\ 1 & 2 & 3\\ 1 & 3 & k \end{bmatrix}\begin{bmatrix} x\\ y\\ z \end{bmatrix}= \begin{bmatrix} 3\\ 6\\ 4+k \end{bmatrix}$$ ...
0
votes
2answers
24 views

Resolve this system:

Im tried to resolve this problem: $$\max\quad f\left( x,y \right) =xy\quad \text{s.a}\quad \begin{cases} x^2 +y^2+z^2 -1=0 \\ x+y+z=0 \end{cases}$$ Well, i form the lagrangian and the respective ...
1
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0answers
17 views

Is there a way to delineate the parameter of highest influence in a system of differential equations?

So I have a system of nonlinear ordinary differential equations dependent on parameters. These equations can traditionally be solved numerically with robust methods and the solution is well defined. ...
3
votes
4answers
95 views

Quick way to solve the system $\displaystyle \left( \frac{3}{2} \right)^{x-y} - \left( \frac{2}{3} \right)^{x-y} = \frac{65}{36}$, $xy-x+y=118$.

Consider the system $$\begin{aligned} \left( \frac{3}{2} \right)^{x-y} - \left( \frac{2}{3} \right)^{x-y} & = \frac{65}{36}, \\ xy -x +y & = 118. \end{aligned}$$ I have solved it by ...
3
votes
1answer
48 views

Fruit vendor selling fruit

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with simultaneous diophantine equations, but other than that, the textbook gave ...
1
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3answers
75 views

Solving a three variable equation

I have three given values, suppose a=1.86, b=2.6 and c=4.2. Now I have to figure out x,y,z such that $x\gt 0,y\gt 0$ and $z\gt 0$ $x+y+z=1$ $a*x\gt 1, b*y\gt 1$ and $cz\gt 1$ I need a ...
1
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1answer
79 views

solve system equation: $ 2a^2 - 1 = b, 2b^2 - 1 = c, 2c^2 - 1 = a $

I have this system equation: $$ 2a^2 - 1 = b $$ $$ 2b^2 - 1 = c $$ $$ 2c^2 - 1 = a $$ From system equation we see that $ a \neq 0 , b \neq 0, c \neq 0 $ , so : $ 2a^2 - 1 \neq 0 => a \neq ...
0
votes
1answer
39 views

Proving that if $ad-bc \neq 0$ then there is an unique solution to the linear system with 2 unknowns and 2 equations

Exercise: Prove that if $ad-bc \neq 0$, then the system $$ ax + by = j \\ cx + dy = k $$ has an unique solution. This is from the very first subsection of Hefferon's Linear Algebra, and also the ...
0
votes
1answer
25 views

Problem with Solve a Differential Equation

I Have a little problem . I wrote this function ( function describe dynamics of ball-hoop system): ...
3
votes
1answer
66 views

System of Equations: any solutions at all?

I am looking for any complex number solutions to the system of equations: $$\begin{align} |a|^2+|b|^2+|c|^2&=\frac13 \\ \bar{a}b+a\bar{c}+\bar{b}c&=\frac16 (2+\sqrt{3}i). \end{align}$$ Note ...
0
votes
0answers
22 views

Finding the Inverse of Polynomial Equations (Approximatly)

Assume one is given a set of two equations of the form: $$x(u,v) = u + a_1 u^2 + b_1 u v + c_1 v^2$$ $$y(u,v) = v + a_2 u^2 + b_2 u v + c_2 v^2$$ And one would like to find the inverse functions, ...
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1answer
35 views

Solution of the equation… [closed]

How to find out the analytic solutions of the equation $1-4\sin^2\frac{\theta}{2}=\frac{\sin\theta(n-1)}{\sin\theta n}$ in the interval $(0, \pi)$? $n$ is an arbitrary integer constant.
1
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1answer
27 views

Positive solutions to a system of linear diophantine equations

A system of equations is $$x_1+x_2+x_3+x_4=b_1$$ $$x_1+x_5+x_6+x_7=b_2$$ $$x_2+x_5+x_7+x_8=b_3$$ $$x_3+x_6+x_8+x_{10}=b_4$$ $$x_4+x_7+x_9+x_{10}=b_5$$ $b_1,...,b_5$ and $x_1,...,x_{10}$ are positive ...
0
votes
2answers
56 views

Computer algebra system for solving systems of partial differential equations / PDEs [closed]

Looking for a symbolic computer algebra system software package, capable of symbolically solving systems of partial differential equations (PDEs). I am certain this can be done with Maple and ...
3
votes
0answers
88 views

System of symmetric equations

I was working on writing some problems for a contest, and I wrote the following system of equations: \begin{align*} x^2+yz&=259,\\ y^2+zx&=217,\\ z^2+xy&=203. \end{align*} Of course, ...
0
votes
0answers
14 views

Generalizing the algebraic nature of linear inconsistent system

I want to know whether solving any inconsistent linear system in any dimension end up in a similar manner that is $0 = a$ where a is non zero. For 2D, the only reason for inconsistent system can be ...
1
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1answer
23 views

Can this system of linear equations have infinite solutions?

$ax_1 + bx_2 + 2x_3 = 1$ $x_1 + x_2 + x_3 = 1$ I'm fairly sure that I cannot, however my exam prep question seems to suggest that it might (perhaps it's poorly worded).
1
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0answers
46 views

How To Solve This Non-Linear System (Ellipsoid-Plane-Cone Intersection)

Any help on how to solve this ellipsoid-plane-cone intersection problem or just even how to approach it will be greatly appreciated. All vectors are in $\mathbb{R}^3$ and I am trying to find ...
0
votes
2answers
31 views

Finding for which value of an unknown a linear system has a single solution

I have a system of linear equations (two equations, two variables) and an unknown coefficient a. I need to find which values of ...
1
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0answers
50 views

Polynomial roots finding algorithm

My initial problem is a parameter estimation problem that is solved by minimining a least-square criterion with the Gauss-Newton algorithm. However finding a good initial iterate is very tedious. ...
0
votes
3answers
23 views

Find the dimension of the vector space of solutions of $3 \times 4$ matrices $N$ where $N^{T}M=0$

Let $M$ be the $3 \times 4$ matrix displayed below $$ \begin{bmatrix} 1 &3&2&4\\ 2&4&3&5\\ 3&5&4&6\\ \end{bmatrix} $$ I want to find the dimension of the vector ...
0
votes
1answer
10 views

Solving a set of $N$ (what I hope may become) linear equations

When faced with $N$ beads on a string, I found the following equation $$-\omega^2A_p+2\omega_0^2A_p-\omega_0^2(A_{p+1}+A_{p-1})=0$$ Where $p=1,2,\dots,N$ and $A_0=A_{N+1}=0$ I know I can't solve for ...
1
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3answers
26 views

Which Coefficient will Make a 2-Variable Linear System Solvable?

This is most likely a pretty simple problem although my textbook doesn't quite explain how to solve it. I have a linear system with two equations and two variables (x and y) below: ...
0
votes
2answers
55 views

trouble with non-homogeneous ODE system… which method shall I use?

I am an undergrad statistics student and I am having troubles with non-homogeneous ODE systems. During my classes I went over just three methods for solving odes: Laplace transform, Fourier transform ...
0
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1answer
29 views

Amount of solutions added to a system of equations through the application of non-invertible operations.

Let's say we had a linear equation of the form $ax+b=c$ we then solve it for $x$ getting, let's say, $x=5$. Just for fun, let's pretend we haven't realized we had solved the problem, so we square ...
0
votes
0answers
55 views

How can I solve this variable-coefficient ODE system?

I originally have a linear, homogeneous, second-order variable coefficient ODE system of this form: $X''(x) = A(x)X(x)$, where $X(x) = $\begin{bmatrix} f(x) \\ g(x) \\ \end{bmatrix} ...
-2
votes
1answer
85 views

Solve system equation: $ \sqrt{a- \sqrt{b}} = \sqrt{c} - 1, \sqrt{b - \sqrt{c}} = \sqrt{a} - 1, \sqrt{c - \sqrt{a}} = \sqrt{b} - 1 $ [closed]

Can you help me how to solve this system equation: $$ \sqrt{a - \sqrt{b}} = \sqrt{c} - 1 $$ $$ \sqrt{b - \sqrt{c}} = \sqrt{a} - 1 $$ $$ \sqrt{c - \sqrt{a}} = \sqrt{b} - 1 $$
0
votes
1answer
41 views

system of equations 3 variables

I should find $A,B$ and $C$. I know answers but can't figure out how to solve it. Anyone? We are to find value of $x^4+y^4+z^4$ when $x, y$ and $z$ are real numbers which satisfy the following ...
0
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1answer
95 views

Solve the equation: $x^3+7x^2+16x+5=(1-2x)\sqrt[3]{-3x^2-7x+5}$

Solve the equation: $x^3+7x^2+16x+5=(1-2x)\sqrt[3]{-3x^2-7x+5}$ I used wolframalpha.com and get the solution: $x\in\{-3;2\sqrt2-3\}$ When $x=-3$, $\sqrt[3]{-3x^2-7x+5}=-1$ When $x=2\sqrt2-3$, ...
0
votes
1answer
27 views

Steady states of a system

How can I find the steady states? I am aware that the condition is to equal 0 but I am not able to say how many steady states there are... $$\begin{cases} \dot x=x-y^2 \\ \dot y= -x+2y-z^2 \\ \dot z= ...
1
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1answer
47 views

Lagrange multipliers problem with two constraints

Hi guys I am working with the following polynomial and I am trying to find the $\lambda , \mu$. I have a polynomial and I am trying to do Lagrange multipliers. Here is what I have. $f(x,y,z)= a ...
3
votes
1answer
100 views

Need help with this proof, I don't understand it , could anyone clarify some of the details. System of linear Differential equations.

$$(*)X'=A(t)X - system$$ $$(*)PX(\alpha)+QX(\beta)=0.$$-border conditions, where P,Q constant square matrices $n \times n $. Let $Y(t)$ be the fundamental matrix for the system $(*)$ normed for$ t= ...
0
votes
0answers
14 views

Inverse of pairing function

I am looking for the inverse of the unordered pairing function: $$ \langle x,y\rangle = xy + \left\lfloor \frac{\big( |x-y|-1 \big)^2}{4} \right\rfloor $$ where $x$ and $y$ are positive integers. ...
1
vote
1answer
25 views

How do you solve this system of equation?

if $J_x= \oint y^2 ds $ and $J_y= \oint x^2 ds $ and $J_{xy} = \oint xy ds $ how I can find $a$ and $b$? $$\left\{\begin{matrix} a.J_{xy}+b.J_x=-M_x\\ a.J_y+bJ_{xy}=M_y \end{matrix}\right.$$ ...
0
votes
1answer
12 views

Let the system $Ax=b$ be incompatible. Prove that $C^kx=0, C=[A,b]$ is determined for all $k\in \Bbb{N}$.

Let $A \in \Bbb{R}^{n \times (n-1) }$ be of rank $n-1$, let $b\in \Bbb{R}^n$. Let the system $Ax=b$ be incompatible. Prove that $C^kx=0, C=[A,b]$ is determined for all $k\in \Bbb{N}$. I can't use ...
0
votes
0answers
60 views

Exact solution to the given system of ODE 1

I'm trying to better understand basic neuroscience systems but I have almost no background in differential equations. Here's the standard leaky integrate-and-fire neuron with conductance based ...