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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5 views

Substitution in a system of ordinary differential equations when terms of the same order derivative for different variables occur in the same equation

Let's say I have a differential equation such as: y'' - 2ty' + y = 0, y(0) = 2.1, y'(0) = 1.0 I can solve this (among other ways) by substitution and conversion ...
1
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0answers
12 views

A system of non-linear equations with a small parameter

Is there any way to solve analytically the following system of equations to the leading order in $\epsilon$: $$\left\{ \begin{array}{rcl} \mu^2 \phi_1 + \lambda \phi_1 (\phi_1^2 + \phi_2^2) + ...
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2answers
55 views

Solving a system of three simultaneous equations

Given the system $$ \begin{align*} -2x + ay - bz &= -4 \\ x + bz &= 2 \\ 2x + y + 3bz &= b \end{align*} $$ The question asks to find conditions on $a$ and $b$ that the system has no ...
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4answers
145 views

How to solve current exponential equation? [on hold]

There is an equation: $$3^x + 7^x = 21^x$$ How to solve this?
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0answers
14 views

How would I get Maple to display all integer solutions to this system of inequalities? [on hold]

I need to find all the integer solutions satisfying: $$20+x\geq0;\space2x+5y\geq;\space-x-2y\geq0.$$ I'm not sure which Maple functions would work and whatnot. A guy can only google this stuff for so ...
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1answer
34 views

How can I solve a system of two equations, like $A + B = 13$ and $2D + B = 13$?

I am currently studying for my SSAT and this question appeared in my practice book: When $A + B = 13$ and $2D + B = 13$, what is the value of $D$? (A) 13 (B) 5 (C) -5 (D) -7 ...
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2answers
75 views

Solve system of 3 equations

$x+y+z=0$ $x^2+y^2+z^2=6ab$ $x^3+y^3+z^3=3(a^3+b^3)$ this is what i reasoned out so far; $xyz=a^3+b^3$ $x^2+zx+z^2=3ab$ $y^2+zy+z^2=3ab$ $x^2+xy+y^2=3ab$ $y^2=3ab+zx$ $x^2=3ab+zy$ ...
1
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1answer
21 views

Cannot figure out a second order lineary differential equation with initial values

I got the following question: Solve the following initial value problem: $y(0) = 0$, $y'(0) = 1$, $$y'' + 10y' + 25y = 0$$ So I started with getting the general solution: $$ y(x) = C_1e^{-5x} + ...
2
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0answers
24 views

$\sum (\sqrt{x_k-k^2}-k)^2=0$ implies $x_k=2k^2$?

Let $x_1,x_2,\ldots,x_n$ be reals numbers such that $$\sum_{k=1}^n k\sqrt{x_k-k^2}=\frac12\sum_{k=1}^n x_k$$ Find all possible $n$-tuples of solution. So, I got the following solution from ...
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3answers
20 views

How to solve this system of equations (Lagrange Multipliers)

I was doing a question on Lagrange multipliers and stucked when trying to evaluate the point. The system of equations that I can't solve is this: $$y^2-x^2+3x-3y=0$$ $$-y^2-yx+3y-xy=0$$ I just ...
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0answers
25 views

GMRES and Preconditioning

I am using GMRES to approximate the solution of a system of equations $Ax=b$, I am using a preconditioner $P$ to make GMRES converge faster. My question is how do I know if the preconditioner I am ...
3
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1answer
154 views

How to solve 29 coupled quadratic equations?

I have a set of 29 coupled quadratic equations, with 29 unknown variables. Can anyone offer any advice on how I could go about solving this? 3 days of staring at a wall has so far given me no ...
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1answer
29 views

What's the solution to this exponential system of equation?

What are the steps to solving a system of equations when $x$ and $y$ are exponents? But they have different base. Here is the problem. $5^x\times3^y=45$ $3^x\times5^y=75$
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4answers
66 views

Solving a homogeneous system of three ODEs with variable coefficients.

I am interested in solving the following system of ODEs: $$ \begin{pmatrix} x'(t) \\ y'(t) \\z'(t) \end{pmatrix} = a \begin{pmatrix} 0 & -B_2 & B_1 \sin \omega t \\ B_2 & 0& -B_1 ...
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1answer
54 views

Solving polynomial equation system to find three dimensional location

For an embedded systems project, I need to solve a system of equations. However, my algebraic skills are limited, and I am not able to solve it. This question consists of the following parts. The ...
2
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2answers
17 views

Finding the nth term in a recursive coupled equation.

I'm probably missing something simple, but if I have the recursive sequence: $$ a_{i+1} = \delta a_i+\lambda_1 b_i $$ $$ b_{i+1} = \lambda_2 a_i + \delta b_i $$ how would I find a formula for $a_n$, ...
2
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0answers
27 views

Why are equilibria so important?

In studying nonlinear systems of differential equations, unlike linear systems, it turns out that we are more interested in equilibrium points rather than general solutions themselves. I mean, look ...
4
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1answer
31 views

linearly independent and determinant

This question says a matrix $\begin{bmatrix}a & b\\c & d\end{bmatrix}$ where $a_{ij}$ are real numbers. I need to prove that $\det|A|=ad-bc\neq0 \iff $the columns are linearly independent. ...
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1answer
33 views

Solving the equations $x_1= 4 x_2$ and $x_3= 5 x_2$, with the sum of all three being $150$

Here is the problem. A set X is partitioned into subsets x1, x2, and x3. The number of elements in x1 is 4 times the number in x2. And the number in x3 is 5 times the number in x2. If n(x)=150, ...
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0answers
37 views

Impossible System of Equations

This is from a competition: DMM Olympiad, Ural State University P4 I don't understand what the question means exactly (the first part, i.e. "exclude $x$ or $y$ from..." part). Does it mean "write $x$ ...
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2answers
50 views

How to solve this Linear Algebra problem involving a system of linear equations?

The following is what I have so far. I'm not sure how to use my echelon matrix to find out which values for the variables can provide an answer to the question or how to prove it. I was thinking ...
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1answer
21 views

Help establishing restrictions for consistency on a linear system.

I'm having trouble wrapping my head around this problems, and others similar to it. I can typically solve systems of linear equations, but some give me trouble, especially dealing with unknown ...
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0answers
31 views

Easily solving a system of equations [closed]

I have a system of equations: \begin{align} d_1 &= 3.9 v_i + 7.605 a \\ d_2 &= 4.9v_f \\ d_1+d_2 &= 100 \\ v_f^2 &= v_i^2 + 2a d_1 \end{align} I know I could rigorously solve this ...
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0answers
24 views

Search Direction in Conjugate Gradient

Could you help me with a Conjugate Gradient question? In using CG to solve $Ax = b$, why is the search direction $p_{k+1}$ in CG chosen as a linear combination of the residual $r_k$ and previous ...
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1answer
25 views

A Set of Linear Equations Equal to Zero

If A+B+C+D = 1; Let A,B,C,D be elements of vector V. Let there be a 4*4 matrix M as such : -5 5 0 0 4 -8 4 0 0 5 -7 2 0 0 10 -10 A property ...
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2answers
41 views

Find Maximum and Minimum value by two polynomial equations

Suppose there are $7$ real numbers say $A,B,C,D,E,F,G$ All we need to find the minimum and maximum value of $G$ satisfying the following two equations :- Sum of Numbers :- $A + B + C + D + E + F ...
2
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2answers
56 views

Find a, b, c if three equations are given?

I was given three equations in term of $a, b$ and $c$. Equations are as follows $ab (a+b+c)=1001$ $bc(a+b+c)=2002$ $ac(a+b+c)=3003$ Find $a, b, c$. MY ATTEMPT I took tue ratio and I got relation as ...
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0answers
13 views

independent nonlinear equations

I am just wondering what the term 'independent equations' means. I found the term in the book of Kolmogorov about the basic notions of probability calculus. After Definition I of Section ...
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1answer
17 views

How get variable values when one of them is within non-trivial radical

Can this be done, and if so, how: Given four constants $(K_i)$ and variables $x$ and $y$, is there a way for me to find the values of $x$ and $y$ when $K_{1-4}$ are known for these two simultaneous ...
2
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2answers
53 views

How to prove, that solution of system $Ax = b$ exists only if there is no solution of $A^T y = 0$ and $b^T y = 1$?

I have a little linear algebra problem here: How can I prove, that there is a solution of system $Ax = b$ only if there is no solution of $A^T y = 0$ and $b^T y = 1$?
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0answers
19 views

Trouble finding the values of a matrix using rref

I'm working on a school project in which I have to get all the values of a missing matrix. To make a small test in my program, I used a simplified example just to see if the math was right, but for ...
4
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1answer
67 views

Find minimum number of sums of $3$ out of $5$ whose vanishing implies all five to be zero

Problem: let $a,b,c,d,e$ be real numbers, now there are $\left(\binom{5}{3}=10\right)$ numbers $$a+b+c,a+b+d,a+b+e,a+c+d,a+c+e,a+d+e,b+c+d,b+c+e,b+d+e,c+d+e$$ Question1:($\textbf{Jérémy Blanc ...
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1answer
23 views

Determinants to solve a system

I was reading a book on Calculus when I came across this: $$\begin{cases} v+\ln(u)=xy \\ u+\ln(v)=x-y \\ \end{cases}$$ $$\begin{cases} \frac1u\frac{\partial u}{\partial x} +\frac{\partial ...
2
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0answers
31 views

suggestion for lyapunov function

Consider differential equation \begin{align}x'&=-t(x+y)\\ y'&=-y+x-y(y^2-6).\end{align} Can some one suggest a lyapunov function for it. I have examined $V(x,y)=x^2+y^2$ , ...
0
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1answer
21 views

Solve for minimum x value in two-variable equation provided a ratio

The equation is: $$500 = 5x - 2y$$ I know the ratio of x to y is $7:3$; what is the minimum possible value of x and how would I approach this question?
0
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1answer
19 views

Understanding Overdetermined System

Consider a system of linear equations $$A \times x = B$$ The system has a unique solution exactly when the determinant of the coefficient matrix (i.e. A) is nonzero. When the determinant of the ...
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0answers
24 views

System of Trigonometric Equations

Could someone please help me with the following system of equations
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1answer
46 views

Is there any algorithm to find the solution of a system of 2 linear and 1 algebraic equation?

I have a system such as: $$\begin{aligned} a_1+b_1t&=u\\ a_2+b_2t&=v\\ a_3+b_3t&=f(u,v)\; \end{aligned}$$ Where a1, b1, a2, b2, a3, b3 are known ...
3
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3answers
60 views

How find this $x_{1},x_{2},\cdots,x_{1994}$ with this following system equation $3+2x_{i+1}=3|x_{i}-1|-|x_{i}|$

Find the all real numbers $x_{1},x_{2},\cdots,x_{1994}$ such $$3+2x_{i+1}=3|x_{i}-1|-|x_{i}|,i=1,2,3,\cdots,1994$$ where $x_{1995}=x_{1}$ It is clear equivalent solve following system equation real ...
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2answers
33 views

Gaussian Elimination Type Method Required

I'm struggling a bit with the following problem: $3 + 14x = 1 + 25y = 9 + 288z$ I have a series of these equations which I need to solve, with different first terms in each case and one of these ...
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6answers
63 views

Simple solution to system of three equations

I've been given the question; $$xy = \frac19$$ $$x(y+1) = \frac79$$ $$y(x+1) = \frac5{18}$$ What is the value of $(x+1)(y+1)$? Of course, you could solve for $x$ and $y$, then substitute ...
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0answers
23 views

How to solve sum of sines and cosines system of equations?

I have a set of equations to solve which in the following form: $ \cos(t_1 + t_2 + t_3 + t_4) + \sin(t_1 + t_2 - t_3 + t_4) + \cos(t_1 - t_4 + t_3 - t_5) + \sin(t_1 - t_2 + t_3 - t_5) + \cos(t_1 + ...
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2answers
48 views

How to solve this system of equations

I just can't seem to get this one.. I know the solutions are $(x, y) = (0, 8)$ (I can find this one) and $(x, y) = (-1, 4)$ but I can't work out how to find $(-1, 4)$. The system is: $$y(4x-y+8)=0$$ ...
4
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2answers
370 views

Can two unknowns of two *unrelated* linear equations be determined?

This question is based on the storm caused by this: https://twitter.com/ddmeyer/status/549965027948507136. Since a twitter discussion is not an objective question, I'll simply write out the key ...
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1answer
30 views

Geometric interpretation of determinant of a system of homogenous linear equations

What is the geometric interpretation of the determinant of a matrix representing a system of homogenous linear equations? We know that iff the determinant is equal to zero the system has a ...
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0answers
82 views

Method of characteristics of a system of first order pdes

Consider the system of first order PDEs $ \left\{ \begin{eqnarray} \frac{\partial}{\partial t} v_1 + \frac{\partial}{\partial x_1} p_1 + \eta(x_1) v_1 = 0 \\ \frac{\partial}{\partial t} v_2 + ...
0
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2answers
41 views

system of equations which share only one variable?

I am trying to build a website that runs on this equation. I know how to solve the equation for two variables that are in both equations but I have no idea how to solve for three variables where the ...
0
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0answers
22 views

Is there a general solution to this phase-shifted system of equations?

This is a (more general) question related to "Estimated solution to system of equations with phase-shifted functions". Given this system of two equations and two unknown functions: $$ y_1(t) = ...
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1answer
26 views

Estimated solution to system of equations with phase-shifted functions

Forgive my first attempt at MathJax. I have a system of $n$ equations of the form $$ v_j(t) = \sum_{i=0}^{m-1} \frac 1 {|\vec p_i - \vec q_j|} u_i \left(t - \frac {|\vec p_i - \vec q_j|} s \right) $$ ...
0
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1answer
34 views

solving systems of equations for m and b when you know they are both positive?

I am trying to make a website that runs off of this equation. I am only in algebra but I am trying to solve a systems of equation where instead of solving for x and y i am solving for m and b. Here is ...