# Questions tagged [systems-of-equations]

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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### Simultaneous equations in non-Euclidean space?

As I recall, one visualizes equations as lines or planes in Euclidean space and the solutions are intersections among these lines, planes or higher-dimensional equivalents. Is there some use to ...
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### How to find $L$ if $L=\frac{c}{(1-L)^a}$

How to find $L$ if $L=\frac{c}{(1-L)^a}$ I was trying to apply log but $\ln L +a\ln (1-L)=\ln c$. How can continued please? Thank you
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### Find all vectors y such that Ax = y is inconsistent

I am given a matrix A, but that is it. The question is to find all vectors y such that Ax = y is inconsistent, where x is a vector as well (no values are given). My first thought is that there is an ...
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### Finding integral points in a rational lattice

Here is a reduced Gröbner basis of a zero-dimensional ideal $I$ in Singular format, one of whose solutions $(q,a,b)$ provides the key numbers in the solution to the Six Disks Problem: ...
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### 4 simultaneous equations, 3 unknowns, How do I know I've found all the solutions?

$$4x-y-z=21$$ $$2x+4y+z=69$$ $$8x+y-z=81$$ $$-4x+7y+3z=57$$ Solutions are $y=30-2x$ and $z=6x-51$ according to wolfram alpha and it's quite simple to get to these solutions and then check that they ...
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### Predict stable or cyclic population variation in dynamical system

Does the Lotka-Volterra model predict stable or cyclic population variation? What determines the amplitude of the cycles predicted by the Lotka-Volterra model? The Lotka–Volterra equations, also ...
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### Determine if weighted graph can be physically constructed, treating weight as Euclidean distance (ie check if subset of distances is self-consistent)

Suppose we want to position some points in space, given that we know at least some of the distances between them. How can we determine if this is possible? And if it is possible, can we determine the ...
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Given a unit square and $n$ identical circles/discs, what is the smallest radius $r_n$ for which the circles can fully cover the square? For $n=4$, the proven minimal solution is $r_4 = 1/(2\sqrt2) \... • 2,101 -1 votes 1 answer 27 views ### Linear Algebra: How do I find the total trips for each area given the 24 hours limit. [See problem below] You run a delivery company, delivering in three different areas of Manhattan, A, B, and C. On average, a trip to the area takes 4 hours, 5 gallons of fuel and you deliver 3 tons of goods. A trip to ... 0 votes 1 answer 26 views ### All numeric solutions of system of nonlinear equations [closed] I want solve 2D system nonlinear equations. First method is multidimensional Newton (derivatives can be computed). It is fast and general. But is not always convergent, especially if I don't know how ... • 129 0 votes 1 answer 20 views ### Necessary and sufficient conditions for an existence of an orthogonal matrix$P~$s.t.$~P^{-1}AP~$is diagonal, using$~a~$which is one of entries of$A$This problem is quoted from the$3rd year transfer exam of math major in the university. \begin{align} a:=\text{real number}\\ A:= \begin{pmatrix} 0&a&2\\ 1&0&2\\ 2&2&3 \end{... 0 votes 0 answers 30 views ### Solutions to systems of quadratic multivariate polynomials with diagonal quadratic forms I am looking for an analytical solution to a system of quadratic equations of the form: \mathbf{x}^T \mathbf{A}_i \mathbf{x} + \mathbf{b}_i^T\mathbf{x} + c_i=0 ~~~~~~~~ i = 1,..,n $$where \... • 19 1 vote 2 answers 54 views ### Solve system for elements of a matrix I have a system of n equations which follows a particular pattern as follows (showing the case n=3):$$\phi = a_1 + \psi_2 a_2 + \psi_3 a_3 \\ \phi = \psi_1 a_1 + a_2 + \psi_3 a_3\\ \phi = \psi_1 ... • 137 1 vote 0 answers 33 views ### Calculate Specific Rotation Matrix to align Vector A to Vector B in 3d? I have a question very similar to this post (that I found quite helpful), but slightly different. Calculate Rotation Matrix to align Vector A to Vector B in 3d? I would like to accomplish the same ... 0 votes 0 answers 26 views ### Solving a system of PDEs with an ODE I want to solve the following system of equations which consists two PDEs and one ODE: \begin{align} \rho_t+v\rho_x &= 0; \newline Y_t+vY_x &= 0 ;\newline v_t &= -\frac{1}{(\... 1 vote 1 answer 56 views ### Solve the nonlinear system with three equations and three variablesx,y,\lambda$.$\begin{cases} \dfrac{x}{\sqrt{x^2+(y-y_A)^2}} + \dfrac{x-x_B}{\sqrt{(x-x_B)^2+(y-y_B)^2}} = 2x\lambda \\\\ \dfrac{y - y_A}{\sqrt{x^2+(y-y_A)^2}} + \dfrac{y-y_B}{\sqrt{(x-x_B)^2+(y-y_B)^2}} = 2y\... 23 views

### Solving system of equations that have an "or" relationship

I have the following problem to solve: Either John and I can do the same number of one-legged squats, OR John can do infinitely more than I can How many squats can I do? I attempted to solve it like ...
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### Is there a general method for finding real solutions to this class of systems of equations?

Fix a positive integer $n$. Let $\mathbf f=(f_1,\ldots,f_n)$ such that for each positive integer $i\le n$: the function $f_i:\Bbb R^{n-1}\to\Bbb R$ is a polynomial function with real [real algebraic?]...
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