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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3
votes
3answers
70 views

Ratio between two numbers is 6:7 and the difference between them is 10. What are the two numbers?

I know the numbers are $60$ and $70$ but I got that by trial and error. Is there some other more logical way to do this problem?
0
votes
3answers
39 views

Chinese Remainder Theorem Finding the Modulo

Find numbers $t,u,v$ so that $33t+2 = 20u+13 = 29v-1 $ This is a Chinese Remainder Theory problem, but the problem I am having is finding what are the appropriate modulo. I figure it is easiest to ...
0
votes
0answers
20 views

Prove this relation

Solve this: $y^2+2=x^3$ or Prove that $y^2+2=x^3 => (x,y)=(3,\pm 5)$ I know that it could be obvious to some of you by trial and error but I need a methodical approach. Thanks in advance!
0
votes
2answers
21 views

Intuition for using vectors in sale related problems

I am reading Linear Algebra from David Lay's book. He gives one example to showcase use of linear combination of vectors : I understand the solution, but I am completely clueless about how to ...
0
votes
1answer
57 views

If $x^a + x^b = x^c + x^d$ how do $a ,b , c , d$ relationship are?

I used to solved these equation style and it's accidentally found an answer from matching $a, b, c,$ and $d$ relationship when $x^a + x^b = x^c + x^d $ (I assume that $ab = cd$) and found that's ...
2
votes
3answers
32 views

Solutions for a system of congruence equations

I have a system $$ \begin{cases} x \equiv 7 \pmod{15} \\ x \equiv 14 \pmod{33} \end{cases} $$ How can I show that the system does not have any solutions? I know that the first implies that $x = ...
1
vote
1answer
18 views

Solving a pair of equations across a data set

I have the following pair of equations: $a = x\cos(k) - y\sin(k),\ b = x\sin(k) + y\cos(k)$ I know that all variables but $k$ are in the set $\mathbb{N}^0$. Given the above, if I know the value of ...
0
votes
1answer
21 views

Strictly positive linear combination of vectors

I have a matrix S of size $m \times n$. How to find a linar combination of the $n$ column vectors of the form: $x = col(1) + \sum_{i=1}^{i=n}{\lambda_i col(i)}$ such that all entries of $x$ are ...
1
vote
1answer
49 views

Can the equation $\mathbf{Av}=\mathbf{b}$ be solved as $\mathbf{v}=\mathbf{A}^{-1}\mathbf{b}$?

Say I have a $3\times 3$ matrix called $\mathbf A$ and a column matrix vector $\mathbf v$ and another column matrix vector $\mathbf b$. If I have the equation $\mathbf{Av}=\mathbf{b}$ where I know ...
0
votes
1answer
38 views

Faisablity of $Ax=b$

Be the following equation $Ax=b$ where $A$ and $b$ have entries over $\mathbb{N}$. $A$ is a full rank matrix of size say $m \times n$. 1) How to check if the equation admits a strictly positive ...
0
votes
3answers
37 views

How to solve greater & less / inequal equation

Two farmers, Eric and Josef where talking. "How many sheeps do you have?" asked Eric. "If I divide my sheeps in $2, 3, 4, 5,$ or $6$ groups, there will always be 1 sheep left." Josef answered. How ...
0
votes
1answer
28 views

Existance of solution of $Ax < b$

How to check if the inequality $Ax < b$ admits at least one solution. Entries of $A$, $x$ and $b$ are taken in $\mathbb{Z}$
0
votes
1answer
42 views

Solve the system of equations for x and y

Solve the system of equations for $x$ and $y$: $$ \left(\frac{x}{8-2y}\right)^2 - \left(\frac{y}{-4}\right)^2=4 \\ \frac{x}{8-2y} + \frac{x}{-2}=1 $$ I used Lagrange multipliers with multiple ...
2
votes
1answer
35 views

Solving a non-linear system of equations

Studying for finals I have come across a result that I understand how the system is derived but I cannot solve the system. I feel like this should be trivial, but I do not know where to go. Through ...
0
votes
1answer
33 views

Converting from Non-basis coordinates to XYZ. Solving system of equations. Error volume

I have multiple points in 3D space. Each point has the distances to 3 points. Those 3 points are: (50,0,0) (0,50,0) (0,0,50) Lets call those distances $dx,dy,dz$ I want to find $x,y,z$ of those ...
0
votes
0answers
34 views

Find constants α,β,γ,δ such that the limit exists

I have to find $\alpha,\beta,\gamma,\delta \in \Bbb R $ such that $$\lim \limits_{x \to 1} f(x) \in \Bbb R$$ where $$f(x) = \begin{cases}\frac{\alpha x^3-(\beta+\gamma)x-(\alpha+\delta)}{(x-1)^2} ...
2
votes
2answers
63 views

solutions to nonhomogeneous system of differential equations with general solution already known

Let's say we have the general solution to $X' = A(t)X$, where $X=(x_1, x_2)^T$. How do you find the general solution to the system $X'= A(t)X + b(t)$ where $b(t)$ is a $2 \times 1$ matrix with two ...
0
votes
1answer
23 views

One solution of a diophantine system

How to find one solution of $Ax = b$, where $A$ is a $(m, n)$ matrix and $x$ a vector of size $(n, 1)$. $A$, $x$ and $b$ are matrices of integers entries. How to check whether is a solution exists?
2
votes
1answer
17 views

Subspace formed by coefficients of a linear equation

Suppose I have the linear equation \begin{align} ax + by = c \hspace{10mm}(1) \end{align} where $(a,b,c) \in \mathbb{R}^3$. Let $W = \{ (a,b,c) \in \mathbb{R^3} : (1)$ is consistent $\}$. Is $W$ a ...
0
votes
1answer
63 views

Question about having periodic solution.

Assume $a>0$ and $b>0$ and $g(x)=0$ when $|x|>1$ , $g(x)=k$ when $|x|\le1$ . Now show that in system of differential equation $$x'=y $$ $$y'=-[2b-g(x)]ay-ay^2$$ if ...
0
votes
0answers
26 views

Algorithm for solving 2PLE

I have a trouble with this article which trats an attack on the Isonorphism Problem with 2 linear secrets. At the end of page 11 the author analizes the properties of a system using a certain ...
0
votes
0answers
34 views

Is there an analytical solution to this system of equations?

$\alpha_i b_i (1-t_i) k_i^{b_i - 1} = \lambda \text{ and } \sum_i \alpha_i k_i =1$. $k_i$ are the variables--they should all take positive values. There may be an arbitrary number of them. This ...
0
votes
0answers
28 views

Coupled Differential equation of second order in matlab

I have a problem solving a system of differential equations of second order in matlab: $$ \left\{ \begin{array}{l l}\frac{d^2y}{dt^2}= \frac{-y}{(x^2+y^2)^{3/2}}\\ \frac{d^2x}{dt^2}= ...
1
vote
2answers
30 views

Laplace transform for IVP not at zero in system of differential equations

Suppose we have a system $\boldsymbol X'=\boldsymbol A\boldsymbol X$. Let's denote the laplace transform of a vector $\boldsymbol Y$ as $\mathscr L\{\boldsymbol Y(t)\}(s)=\boldsymbol y(s)$. If we ...
1
vote
0answers
45 views

Solve this equation

I have the conditions $$1 = e^{\alpha-1} \sum_{n=1}^M e^{\beta E_n + \gamma N_n} $$ $$\langle E \rangle = e^{\alpha-1} \sum_{n=1}^M E_n e^{\beta E_n + \gamma N_n} $$ $$\langle N \rangle = e^{\alpha-1} ...
3
votes
4answers
161 views

System of congruence equations

I have a system of congruence eqs $$ \begin{cases} x \equiv 14 \pmod{98} \\ x \equiv 1 \pmod{28} \end{cases} $$ I have calculated $\text{gcd}(98,28) = 14$. I can from the congruence eqs get $x = ...
0
votes
0answers
21 views

Deciphering game formula

Hello I'm trying to find a Formula of a certain system(Game) and would like some help. I will try not to get into the context of the game too much, but some times it will be necessary for better ...
0
votes
0answers
20 views

Fastest way to solve specified system of nonlinear equations

I have a following system of equations \begin{equation} \begin{aligned} \sum\limits_{i = 1}^3 g_i V_{i, x} & = (\sum\limits_{i = 1}^3 g_i n_{i, x})t + P_x \\ \sum\limits_{i = 1}^3 g_i ...
0
votes
1answer
56 views

Solve nolinear system of equaion with c/c++ [closed]

My system of equation is like this: (x-a1)^2 + (y-b1)^2 = c1 (x-a2)^2 + (y-b2)^2 = c2 I know it is simple using matlab: ...
1
vote
1answer
38 views

Finding solutions of system of differential equations with eigenvectors

I was trying to solve this system of differential equations: $$\frac{dx}{dt}=3x-y-z$$ $$\frac{dy}{dt}=x+y-z$$ $$\frac{dz}{dt}=x-y+z$$ I found the eigenvalues: $\lambda_1=1,\lambda_2=2$. The ...
0
votes
0answers
21 views

Non-linear system of exponential equations with 2 boundary conditions: $p(y_m)=p_m$ and $\frac{dp(y)}{dy}$

I have this equation: $$ p(y) = -\left(e^{-\tfrac{K_{py}zy}{p_u+c e}}-1\right)\left(p_u+c e^1\right)-c\left(1-e^{-y}\right)^d\left(e^1-e^{1-y}\right) $$ The two unknowns are $c$ and $d$ and the system ...
2
votes
1answer
23 views

When does a linear system have infinitely many solutions, yet some of them don't depend on the others?

Consider this system: $$ \begin{cases} w + x + y + z = 1 \\ w + x + y + 2z = 2 \end{cases} $$ Its solution set is $\{z = 1,\, y= -w - x \;|\; w,\,x \in \mathbb{R}\}$. So, $z$ is "fixed," in a sense. ...
0
votes
1answer
19 views

How were these two equations rearranged to this from?

$$f(x)=F(x)+G(x)$$ $$g(x)=-cF(x)+cG(x)$$ To: $$F(x)= \frac{1}{2}f(x)-\frac{1}{2c}g(x)$$ $$G(x)= \frac{1}{2}f(x)+\frac{1}{2c}g(x)$$ I can kind of see the relationship between the equations but if ...
1
vote
1answer
25 views

Determine parameter so that the absolute value of real solution of the equation is larger than the modulo of complex solution

Given the equation: $$x^3+x+\lambda=0$$ determine real parameter $\lambda$ so that the real solution is greater by absolute value than modulo of the complex solutions. My attempt: Let $x_1$ be the ...
0
votes
1answer
37 views

Roots of an equation using Maple

I am using Maple to find the roots of a non-linear equation in one variable. When I solve the equation, I get only 2 negative roots whereas if I plot the graph of the function, it also shows that the ...
0
votes
1answer
26 views

Building an nth order ODE in Maple (or Matlab)

The question is simple: given a system of ODEs, how can one construct the equivalent nth order ODE in Maple? In my case I have $$ \begin{cases} y''(t)+x'(t)+x(t)=f(t)\\ y''(t)+z''(t)+z'(t)+z(t)=0\\ ...
0
votes
1answer
33 views

Finding initial conditions for which solutions to IVP are periodic

I have an initial value problem $\mathbf x'=A\mathbf x$ $$A = \begin{pmatrix} 1 &1 &0 &0 \\ 3& -1 &0 &0 \\ 0 &0 &0 &-2 \\ 0 &0 &2 &0 ...
2
votes
0answers
60 views

Study of a system of differential equations

I'm asked to study everything that is possible to know about the sytem$$\begin{cases}x'=x^2-y^2\\y'=2xy\\z'=-z\end{cases}$$ My questions here is, how much can be know about it?, how do I know I ...
3
votes
1answer
98 views

Linear system for which the solution space is spanned by the given vectors

Make a system with $3$ equations and $3$ unknowns of which the solution space $V$ is spanned by the column vectors: $$\begin{bmatrix} 1 \\0 \\-1\end{bmatrix},\quad \begin{bmatrix}1 \\3\\ ...
0
votes
1answer
20 views

Help solving system of linear equations.

In the process of running through an algorithm, I have derived the following systems of equations: i) $1/3 + 1/3x_1 + 1/3 x_6 = x_5$ ii) $1/2 + 1/4 x_6 = x_1$ iii) $1/2 + 1/2 x_5 = x_6$ I've tried ...
0
votes
0answers
19 views

On Farkas's Lemma and Existence of a particular solution

This is a real life problem. I have a matrix $A$ which is $m\times n$. I want to check for the conditions on the existence a vector $x\in\mathbb{R}^n$ such that $A x \geq 0$. The Farkas's Lemma, as I ...
1
vote
2answers
36 views

Find $\log_c{x}$ if $\log_a{x} = p$, $\log_b{x} = q$, and $\log_{abc} {x} = r$.

Given that $\log_a{x} = p$, $\log_b{x} = q$, and $\log_{abc} {x} = r$, find the value of $\log_c{x}$.
0
votes
1answer
45 views

Solving a simple systems of equations

Update: 1) As @Amzoti mentioned, I made a mistake in the mathematica code. There should be spaces between x, y and z. So now the following code works: ...
2
votes
1answer
59 views

Stability of nonlinear system of PDE's

Let's assume system $$ \tag 1 \frac{\partial \mu}{\partial t} = \gamma (\mathbf B \cdot \mathbf E), $$ $$ \tag 2 [\nabla \times \mathbf E] = -\frac{\partial \mathbf B}{\partial t}, $$ $$ \tag 3 ...
0
votes
3answers
34 views

Find couples of complex numbers

I found this exercise, given: $$u=|z|+|u|$$ and $$z=|u|+1$$ (it is a system I don't how to write it in latex from) I have to find the couples of complex numbers $u,z$ that comes from the two equation. ...
0
votes
0answers
16 views

Find a matrix and a vector using partial derivative and system of matrices.

Let $f(x)$:=[$f_1(x),...,f_d(x)]^T$ and suppose that |$\frac{\partial^2 f_i(x)}{\partial x_j \partial x_k}|$$\le$K for all $i,j,k$=1,...,d and $x\in\Re^2$. Show how to define an $dxd$ matrix $J(y)$ ...
0
votes
2answers
42 views

Solve system of equations

Are there any good resources for solving systems of equations out there? I tried to put this into wolfram alpha, but it doesn´t seem to work: ...
3
votes
1answer
38 views

Polynomial curve fit

Well I have a 2 (or 3) data points - and some extra limits - and a polynom needs to be fitted through those points (exactly). The polynom needs to be of the smallest order, and not a least square, it ...
2
votes
3answers
35 views

Prove that one of x,y,z is smaller than 3 and one is bigger than 5 if…

If $x+y+z=12$ and $x^2+y^2+z^2=54$ then prove that one has to be smaller or equal to 3 and one has to be bigger or equal than 5. So I got that $xy+yz+zx=45$ and with that I had a function with x,y,z ...
0
votes
4answers
54 views

Solve system of equations

$$\sin(x+y)+1.6x=0$$ $$x^2+y^2=-1$$ Can this system be solved? Please help me with it. I managed to make graphs of it but can't get it solved without graph. Graph: