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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0
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1answer
27 views

Find a basis and the dimension of the solution space W of the following homogeneous system [closed]

Good morning, I need help with this problem. Find a basis and the dimension of the solution space $W $of the following homogeneous system $\begin{cases} x+2y-2z+2s-t=0\\ x+2y-z+3s-2t=0\\ ...
3
votes
2answers
310 views

Solve 6 simultaneous equations for 8 variables puzzle

How to solve this puzzle? The image was sent to me with a caption in Chinese (解了一天了 帮帮忙吧… - googling leads to some solutions) and blank spaces where I have added letters. Separating each row and ...
-1
votes
1answer
40 views

Finding a and b from $a+b/3 = 1$ and $a/2+b/4=3/5$

I have two equations of which I need to solve for $a$ and $b$. $$ a+b/3=1\\ a/2+b/4=3/5 $$ Find $a$ and $b$.
4
votes
2answers
128 views

Prove that this system of linear equations generates $\left| \left( \begin{matrix} 1/2 \\ n \end{matrix} \right) \right|$ as a solution?

This infinite system of linear equations: $$ \begin{array}( 2x_1=1 \\ 3x_1+4x_2=2 \\ 4x_1+5x_2+6x_3=3 \\ \cdots \end{array} $$ In other words, this is particular case of a system: $$ \begin{array}( ...
0
votes
1answer
30 views

Problem of simplification

When trying to solve the equation $y^y = \frac{\ln^{y(1+c)}n}{n}$ , I've found the result $$y=\frac{-\ln n}{W(-\ln^{-c}n)}$$ where $c$ is a positive constant and $W$ is the Lambert function. The ...
0
votes
1answer
21 views

Using Cramer's Method

How do I use Cramer's method to solve the following system of equations ? 2x+2=10 2y=2 2-3y=6x I've solved for y using standard simultaneous equations but this didn't help
0
votes
2answers
32 views

Solving simultaneous equation without dividing by $x$

I have the following equations: $$3x^2 \dfrac{\partial x}{\partial u} + 3y^2 \dfrac{\partial y}{\partial u} = 1$$ $$y\dfrac{\partial x}{\partial u} + x\dfrac{\partial y}{\partial u} = 1$$ where I ...
-1
votes
1answer
16 views

Nonlinear autonomous system of differential equation [closed]

I have the following differential system : $x' = \frac {x^2}{(y-1)}$ $y' = x+1$ By elimination method things get ugly, so how could I solve it?
0
votes
0answers
14 views

Solving Non-Linear Simultaneous Equations

Equation 1: $$ L_{5}^{2} = (C_0 - C_2)^2 + (C_1 \cdot \sin(\theta_2) - C_3 \cdot \sin(\theta_1))^2 + (C_1 \cdot \cos(\theta_2) - C_3 \cos(\theta_1)))^2 $$ Equation 2: $$ L_{7}^{2} = (\lambda \cdot ...
2
votes
2answers
39 views

Do four points lie on the circumference of a single circle? Can I solve this with matrices?

I think I managed to figure out a way to determine whether three points lie in a single line via matrix determinants (but correct me if there's a problem): Where $y - mx - b = 0$, I plug each of the ...
0
votes
1answer
33 views

solution of system of polynomials

I have 3 equations as following: $$ \left\{ \begin{array}{c} (\Delta_{11}*y^2 + \Delta_{12}*y + \Delta_{13})x^2 + (\Delta_{21}*y^2 + \Delta_{22}*y + \Delta_{23})x + \Delta_{31}*y^2 + \Delta_{32}*y + ...
0
votes
1answer
16 views

Jacobian of a system of equations

I'm asked to compute the Jacobian of a system of equations $x_1^4+x_2^4-1=0$ $x_2-\sin(5x_1)=0$ $x_1-x_3^2=0$ What's the Jacobian of a system of equations? Do I perhaps need to infer the individual ...
0
votes
1answer
15 views

How to combine equations on xy plane with those on yz and zx plane?(diagram included)

I am considering a situation, where a cylinder is placed horizontally, like this (b(t) is the minimum distance between the circle and the ground) so, in the xy plane, I have the equation of a ...
0
votes
1answer
25 views

Method of undetermined coefficients for non-homogeneous linear system with two constant vectors

Suppose I have a system of non-homogeneous linear first order differential equations: $$ x'=A x+b_0+b_1t $$ Where $A$ is a $2\times2$ invertible matrix, $b_0$ and $b_1$ are: $$ b_0 = ...
1
vote
0answers
60 views

Analytic solution for system of trigonometric equations

I have two equations as follows: $$ \left\{ \begin{array}{c} (\Delta_{11}\cos(\alpha) + \Delta_{12})\cos(\theta) + (\Delta_{21}\cos(\alpha) + \Delta_{22})\sin(\theta) = \Delta_{31}\sin(\alpha) + ...
3
votes
0answers
37 views

An equation over a finite field

Suppose $x,y,z,w \in \mathbb{F}_{q^2}$, where $q=p^k$ for some prime $p$. Consider the system of equations $$ \left\{ \begin{array}{l} xy + zw = 0; \\ xy^q + yx^q + zw^q + wz^q = 0. \end{array} ...
0
votes
0answers
28 views

How to represent a system of quadratic equations in matrix form

Suppose I have two quadratic equation like the following: $2x^2 - 3x + 2$ $x^2 + 5x + 6$ I want to find the minimum values of these equation with the constraint that: $-3 \lt x \lt 5$ How ...
0
votes
1answer
26 views

Find a system of recurrence relations

Find a system of recurrence relations for the number of $n$-digit binary sequences with $k$ adjacent pairs of $1$s and no adjacent pairs of $0$s. Any help on how to go about doing this would be ...
0
votes
0answers
11 views

Constructing a formula

I have two matrices A,B each item in A is tested against all items in B. If (a,b) matches then I have to calculate a weight for ...
2
votes
2answers
73 views

What can we do to solve the following equation with $6$ variables with some information provided?

Q) There are unique integers $a_2, a_3, a_4, a_5, a_6, a_7$ such that $$\frac{a_2}{2!}+\frac{a_3}{3!}+\frac{a_4}{4!}+\frac{a_5}{5!}+\frac{a_6}{6!}+\frac{a_7}{7!}=\frac 57$$,where $0\le a_i < i$. ...
1
vote
1answer
32 views

Solve this system using elimination for $x(t)$, $y(t)$

Here are my system of equations: $$x'+y'-x=5$$ $$x'+y'+y=1$$ I rearranged them like so: $$x=x'+y'-5$$ $$y=1-x'-y'$$ I took the derivative of $$x=x'+y'-5$$ and got $$x'=x''+y''\Rightarrow ...
0
votes
4answers
35 views

How do I solve system if $2y−z=0$ and $2x+y−z=0$? [closed]

How do I solve system if $2y−z=0$ and $2x+y−z=0$?
0
votes
0answers
21 views

Basic linear system of equations clarification

I am trying to get a solid handle on linear systems of equations and I wanted to know if my following summary is correct. Linear systems of equations $Ax = b$ can either be square, overdetermined or ...
2
votes
1answer
105 views

Solving a system of algebraic and transcendental functions

I am attempting to solve a puzzle (LINK). As I have only taken up to multivariable calc, my college course knowledge hasn't helped. How do you solve a system of algebraic and transcendental functions? ...
0
votes
1answer
29 views

How to use elimination to solve a system of equations with 3 variables

I asked this question before but with a linear algebra angle, however, I need to solve it using the elimination method. I have been able to solve for $y$, which is $y=\frac{-y''}{2}+\frac{3y'}{2}$, ...
0
votes
0answers
19 views

Analytical Case Differentiation

is there a analytical way for case differentiation? In my case a MonteCarlo Simulation calculates a system of equations. Parameters can randomly change so that the underlied mathematical condition ...
0
votes
1answer
57 views

Explain this complex number simultaneous equation step. [closed]

The explanation appears on this web page: OPs problem question Following through, I see everything until the move linking these two steps: $15a - 10b = 7a - 6b$ $8a = 4b$ What mathematical logic ...
0
votes
2answers
38 views

Simultaneous trigometric equation with three angles; how to find two of them?

\begin{cases} P\cos a + Q\cos b + F\cos c = 0 \\ P\sin a + Q\sin b + F\sin c = W \end{cases} I am trying to find $a$ and $b$. My initial attempt was using the identity $\sin a = \sqrt{1 - \cos^2 ...
0
votes
1answer
37 views

Use elimination to solve this system for $x(t)$, $y(t)$, and $z(t)$

So I took linear algebra a few years ago, so I'm a little rusty on how to do ref and rref, but I imagine it can be used to solve this. I just don't understand my output. Here is the system of ...
0
votes
0answers
31 views

How do I solve system of linear equations with 4 variables?

We have system of linear equations $A\vec{x}=b$ : $A=\begin{pmatrix} 2& 1& -1& -1& 1& \\ 1& -1& 1& 1& -2& \\ 3& 0& 0& 0& -1& \\ ...
1
vote
1answer
34 views

Finding y(t) as the solution of x' = Ax

If I have a matrix A = \begin{bmatrix}2&0\\0&3\end{bmatrix} and I am trying to find the solution y(t) to x' = Ax (Solution: x(t) = x(t), y(t)), how should I go about it? I have an initial ...
-1
votes
1answer
34 views

How to calculate the transfer function from a group of equations below?

The group of equations below describe the relationship of variables from a circuit(C stands for capicator, L is for inductor etc.). And the equation at the bottom shows how the transfer function is ...
3
votes
2answers
64 views

Solve this system of equations using elimination for $x(t)$ and $y(t)$

I'm taking an online Differential Equations class and don't understand how to solve this system of equations using elimination. I tried the typical algebraic method but am running into trouble: ...
0
votes
0answers
32 views

Solving for $G(x,y)$ in a Gradient System (Differential Equations)

If I'm given the following, how would I solve for $G(x,y)$? $$\begin{align}\frac{dx}{dt}&=y^2-\cos x\\ \frac{dy}{dt}&=2xy-\sin y\end{align}$$ I know $x'$ is equal to the partial of $G$ with ...
0
votes
0answers
7 views

Large sparse matrix system of linear equations: finding one particular variable from the solution vector

I have an approximately $10000$ by $10000$ matrix with less than $1$% of non-zero elements. Also I don't need to find full solution vector, but only one particular variable from it. Any hints on how ...
0
votes
1answer
21 views

Eliminate a parameterization from system of equations

Let $x(t) = x_0 e^{\lambda_1t} $, $y(t) = y_0 e^{\lambda_2t} $ A book I am reading has performed the following change to remove the parameter $t$: Let $y = cx^{\lambda_2 / \lambda_1}$ where $c = ...
0
votes
2answers
44 views

Solving a feasible system of linear equations using Linear Programming

I am wondering if one could solve a feasible system of linear equations using a Linear programming approach, instead of standard linear algebra techniques such as gaussian elimination. For instance, ...
2
votes
0answers
22 views

Solving A System Of ODE's On MAPLE 17

I Have the velocity fields for two vortices that are located at two different points ${\bf{x_1}}(x_1,y_1)$, ${\bf{x_2}}(x_2,y_2)$ $\vec{V_1} = (u_1,v_1) = \frac{\Gamma_1}{2\pi}\frac{1}{(x-x_1)^2 + ...
-3
votes
1answer
12 views

Solving Problems using Simultaneous Equations

Suzuki and Amin scored s and m marks, respectively , in a test. Their total score is 156 marks.If twice of Amin's score is 57 marks more than Suili's score,find Suili's score
0
votes
2answers
18 views

Variable System of Equation

Suppose we have three systems of three linear equations $E_1$, $E_2$ and $E_3$ such that $$aE_1+bE_2=E_3$$ and $$cE_2+dE_3=E_1$$ where $a$ and $b$ are non-zero constants. Express $c$ and $d$ in ...
1
vote
1answer
42 views

How to solve system of equations containing summation over variable to solve for?

How do we solve for $\pi_i$ in the following? $$\pi_i=\frac{\sum\limits_j N_{i,j}}{\sum\limits_j\left( \ell_{i,j} \frac{\sum\limits_k N_{k,j}}{\sum\limits_k \ell_{k,j} \pi_k}\right)}\qquad\forall ...
0
votes
0answers
19 views

How to solve system of equations with summation constraint?

Not even sure if that title makes sense, but how do we solve for $\pi_i$ in: $$\pi_i=\frac{\sum_j N_{i,j}}{\sum_j \left[{l_{i,j} \frac{\sum_k N_{k,j}}{\sum_k {\left(l_{k,j} ...
0
votes
5answers
64 views

How to verify that one of equations in a polynomial system is redundant?

I know that system of polynomial equations $$ p_1(x_1,\dots,x_n)=0,..., p_N(x_1,\dots,x_n)=0 $$ has infinitely many solutions. I computed some of them numerically and notices that they always satisfy ...
0
votes
0answers
16 views

Solving this system of equations of reciprocals?

Following on from How to solve this system of equations containing reciprocals?, my system of equations has become: $p_i = \frac{b_i}{b_i + l_i+mr_i}$ where $i\in\mathbb{Z}$ $b_i, l_i, r_i >0$ ...
1
vote
0answers
32 views

Isolating roots of polynomial system

I would like to isolate the regions which contain the roots of a system of two bivariate cubic polynomials. I thought I would project the solutions onto $x$ and $y$ axis by means of resultant ...
2
votes
2answers
55 views

Can the system of equations be extracted from its solution?

While I was solving the secondary school exam of 2014 I came across a question that states: After solving those equations: $a_{1}x + b_{1}y = c_{1}$ and $a_{2}x + b_{2}y = c_{2}$, we found that x = ...
0
votes
1answer
20 views

About Duffing equation

Is there a relation between Duffing equation and Van der Pol equation? My second question is what is the application(s) of stochastic Duffing equn. in practice ?
0
votes
2answers
32 views

Basic algebra question. Find W in a system with 3 other unkowns and 2 equations.

I suspect this is a ratter dumb question, but I just want to be sure. I need to find W in the following equation: $$W=\frac{3}{2}x+\frac{6}{5}y+\frac{2}{7}z$$ And the only thing I know is: ...
0
votes
1answer
69 views

I can't solve this Algebra 1 equation: For how long did she run?

Before going to school, Eudora ran from her home to a secret laboratory at an average speed of 12 km/h. Since she was running late, she then took one of her jetpacks and flew to her school at an ...
2
votes
1answer
30 views

Finding the two points on a heart curve which have maximal distance between them

How do I find two points on this curve that have maximal distance between them? I tried to use Lagrange multiplier to solve this, but solve equations is diffcult.