# Tagged Questions

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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### One equation that fits other/multiple equations

I have three equations, one linear, one powered, and one a 2nd order polynomial. Say these equations are: $0.5065x^{2.5066}$, $-11.185x^2+2325.1x-83917$, $729x-28736$ Edit: These are functions, ...
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### Finding non-trivial solutions for the system of linear algebraic equations

Suppose we have a system of $n$ linear algebraic equations where $n>1$ is a positive odd integer. The matrix $A=\{a_{ij}\}_{i,j=1}^n$ of this system has the following properties: $a_{ii}=0$ for ...
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### Is power-associativity an equational property?

A magma $M$ is said to be power-associative if the subalgebra generated by any element is associative. This can be written simply as $x^mx^n=x^{m+n}$ for all $m,n$ positive integers and $x\in M$, ...
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### how to solve an matrix equation that is similar to a sylvester equation

during an algorithmn, I have to solve an equation of the form $$AXD-XBD=C$$ with $A\in\mathbb{R}^{n\times n}$,$X\in\mathbb{R}^{n\times m}$,$B\in\mathbb{R}^{m\times m}$,$D\in\mathbb{R}^{m\times p}$ and ...
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### Solving Quadratic system of equations

Solve this system of equations: $$(1) \quad 0=-10x^2-9xy+50x-25y-7y^2+5$$ $$(2) \quad 0=-5x^2-17xy+25x+50y-14y^2+7$$ Shame on me but I'm failing to solve this system. I can't see a short (...
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### How to solve this system of non-linear equations of second order?

I have a system of three equations: $$a_1- (b_1x+cx^2-cx) + (dx - x^2 + x) - yz = 0$$ $$a_2- (b_2x+cx^2-cx) + (dx - x^2 + x) - (y+1)z = 0$$ $$a_3- (b_3x+cx^2-cx) + (dx - x^2 + x) - (y+2)z = 0$$ ...
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### Solve for $x,y,z$ from the linear equations.

The main question is : \begin{align} (b+c)(y+z)-ax &= b-c \tag{1} \\ (c+a)(z+x)-by &= c-a \tag{2} \\ (a+b)(x+y)-cz &= a-b \tag{3}\\ \end{align} Solve for $x,y,z$ if $a+b+c\ne0$ ...
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Suppose now system of differential equations, namely, $$$$\ddot{y}(t) + \omega^{2}y(t) = \dot{z}(t) \\ \dot{z}(t) = (-A+\dot{y}(t))z(t)$$$$ I want to check, for which $y(t)... 0answers 11 views ### System of nonlinear first order pde's I need a reference to results on existence of solutions to systems of nonlinear first order PDEs. to be more precise I am interested in the following: Let$F\colon\mathbb{R}\to \mathbb{R}^d$be a ... 1answer 71 views ### Find solutions of$a + b + c$even,$3a + 2b - 3c$odd,$a - 7b + 8c$odd, in polynomial time Suppose I have a linear equation in$3$variables$a$,$b$and$c. \begin{align} \begin{cases} a + b + c &= 40 \\ 3a + 2b - 3c &= 49 \\ a - 7b + 8c &= 77 \end{cases} \end{align} The ... 1answer 30 views ### Geometric interpretation of a linear system Solve the following system of linear equations in terms of parametera\in\mathbb R$and explain geometric interpretation of this system:$ax+y+z=1,2x+2ay+2z=3, x+y+az=1$. By Cronecker Capelli's ... 0answers 17 views ### Continuity of solution of a system of nonlinear equations I have a system 3 non-linear equations with 3 variables$x,\ z,\ N$and two parameters$L$and$t$. $$\{x,\ z,\ N,\ L,\ t\}\geq0.$$ Equations are smooth (at least C1) in variables and parameters. This ... 3answers 63 views ### Prove that there are exactly$k$pairs$(x,y)$of rational numbers with$0\leq x,y<1$for which both$ax+by,cx+dy$are integers. Let$a,b,c,d$are integers such that$(a,b)=(c,d)=1$and$ad-bc=k>0$. Prove that there are exactly$k$pairs$(x,y)$of rational numbers with$0\leq x,y<1$for which both$ax+by,cx+dy$are ... 1answer 24 views ### Existence of solution to underdetermined linear system with variable coefficient matrix. I'm trying to think through a network flow problem, and while I could probably shuffle this into a form that a linear programming method would work, it feels like there ought to be something more ... 0answers 92 views ### Is a finite number of quadratic equations in two variables sufficient to solve for the two variables? Let's say I’m trying to solve a Diophantine problem in two positive integers,$y$and$q$. Furthermore, let’s say I can derive an extremely large (read: arbitrary) number of equations of the form $$ay^... 2answers 60 views ### Solve an overdetermined system of linear equations I have doubt to solve this system of equations \begin{cases} x+y=r_1\\ x+z=c_1\\ x+w=d_1\\ y+z=d_2\\ y+w=c_2\\ z+w=r_2 \end{cases} Is it an overdetermined system because I see there are more ... 0answers 13 views ### The relationship between simultaneous equations model and seemingly unrelated regression model? recently I try to solve a equations-system. So after read few pieces of paper, I want to use SUR model. Based on what I read, those paper notes that usually equations-system has two method to be ... 0answers 6 views ### Find the relation between mean and variance for lognormal distribution giving as input mean and standard deviation of normal distribution I am working with a Lognormal distribution with mean m and variance v. I give as input \mu and \sigma of the relative normal distribution in order to calculate the cumulative Lognormal. Now, ... 0answers 20 views ### A system of two Riccati equations I am trying to solve the following system of two non-linear Riccati-type differential equations:$$ \dot{x} = (1-x)\left(p^{x} + q^{x}x + qy\right), \\ \dot{y} = (1-y)\left(p^{y} + q^{y}y + qx\right)... 0answers 24 views ### system of inequalities in Mathematica I am trying to solve the following system of inequalities in Mathematica but the output is just the same system of inequalities. I need to get the expressions for x, y in terms of the pi indexed ... 1answer 26 views ### Counting solutions by estimating Fourier coefficients In W. T. Gower's essay The Two Cultures of Mathematics, he mentions the following as an example of a 'general principle' in combinatorics: "If one is counting solutions, inside a given set, to a ... 1answer 43 views ### compare$x^{y^{z}}$and$y^{x^{z}}$(help) the problem goes like this : let$(x,y,z) \in \mathbb{R^3}_{+}$and$0<x<y<z$compare$ x^{y^z}$;$x^{z^y}$;$y^{x^z}$;$y^{z^x}$;$z^{y^x}$;$ z^{x^y}$how can we compare the values ? 2answers 48 views ### Solving equations system:$xy+yz=a^2,xz+xy=b^2,yz+zx=c^2$Solve the following system of equations for$x,y,z$as$a,b,c\in\Bbb{R}\begin{align*}xy+yz&=a^2\tag{1}\\xz+xy&=b^2\tag{2}\\yz+zx&=c^2\tag{3}\end{align*} My try: Assume thatx,y,z\...
Consider the equations: $$\begin{split} x^3 + x e^y + \sin(z) &= 0\\ z^2 + y\cos(x) &= 0 \end{split}$$ in a neighborhood of $(x_0, 0, 0)$ with a suitable $x_0$ by $(y, z)$ resolve, that ...
How to prove that a congruence system with $n$ equations can be solved if and only if all the equations can be solved two by two? \begin{cases} x \equiv a_1 \phantom ((mod\phantom mm_1) \\ x \equiv ...