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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4
votes
2answers
32 views

System of 3 differential equations

I'm trying to solve this system $$x'=x-3y+3z$$ $$y'=-2x-6y+13z$$ $$z'=-x-4y+8z$$ must be reduced to a single equation I tried to express the x 3 and substitute in the other two but then I have not ...
2
votes
3answers
79 views

Can systems of 3 linear equations with 3 unknowns have more than one solution?

In each part,determine whether the given vector is a solution of the linear system \begin{align} 2x-4y-z&=1\\ x-3y+z&=1\\ 3x-5y-3z&=1 \end{align} (a) $(3,1,1)$ (b) $(3,-1,1)$ (c) ...
5
votes
2answers
75 views

Solve this equation: $(x+2)(\sqrt{2x+3}-2\sqrt{x+1})+\sqrt{2x^2+5x+3}=1$

Solve this equation: $(x+2)(\sqrt{2x+3}-2\sqrt{x+1})+\sqrt{2x^2+5x+3}=1$ This is my try Let $t=\sqrt{2x+3}-2\sqrt{x+1}$ or $t^2=6x+7-4\sqrt{2x^2+5x+3}=1$ The equation is equivalent to: ...
3
votes
3answers
48 views

Solve the non-linear system of equations

For real $x,y,z>0$ solve the system of equation \begin{cases} \dfrac{1}{x}-3 y+4 z=5,\\ \dfrac{1}{y}-4 z+5 x=3,\\ \dfrac{1}{z}-5 x+3 y=4, \end{cases} It is easy to check out that $$ x ...
0
votes
0answers
29 views

When to use iterative methods for solving systems of linear equation

Iterative methods such as Jacobi, Gauss-Seidel method and successive over relaxation have a very limited field of use - for diagonally dominant matrices. So how they could be used on practice? What is ...
0
votes
3answers
73 views

The system of differential equations is in steady state

We have a system of non-homogeneous differential equations $$X'=AX+B$$ What does it mean that the system is in steady state?? $X$ is the vector $\begin{pmatrix} x_1(t) \\ x_2(t) \\ ...
0
votes
1answer
32 views

system differential equation 11

The system in the symmetric form is given by $$\frac{dx}{x^2-y^2-z^2}=\frac{dy}{2xy}=\frac{dz}{2xz}.$$ Rewrite using the derivatives $$\frac{dx}{dt}=x^2-y^2-z^2,$$ $$\frac{dy}{dt}=2xy,$$ ...
1
vote
0answers
61 views

Simple $\{-1,0,1\}$ equation set

I'm trying to find the shortest path, getting from $x=0$ to $x=k$ in a certain problem, where I can slowly accelerate and decelerate. It comes down to finding the smallest $n$ and set of values ...
0
votes
0answers
15 views

Optimal initial guess in Newton-Raphson method for nonlinear systems [on hold]

I would like to know what is an optimal initial guess for use with Newton-Raphson method for nonlinear systems. Thank you for your help.
2
votes
3answers
118 views

How was the determinant of matrices generalized for matrices bigger than $2 \times 2$?

How was the determinant of matrices generalized for matrices bigger than $2 \times 2$? I read a book a very long time ago where it said something like this: Given a system of two equations with two ...
2
votes
1answer
29 views

Calculate tangent points of two circles.

I have 2 circles with given center coordinates and radius. And now I need to find the coordinates of all 8 tangent points to those circles? I found this site explaining exactly what I want do to: ...
0
votes
2answers
15 views

Constructing Simultaneous Equation for This Problem

Suppose we have a rating system where a "thumbs up" equals +1 and a "thumbs down" equals - 1. We know the total number of votes cast and the current score. For example a score of +3 with 5 votes cast. ...
1
vote
1answer
33 views

A system of simultaneous equations

I'm currently stuck solving this set of equations. $$x(x+y+z)=4-yz$$ $$y(x+y+z)=9-zx$$ $$z(x+y+z)=25-xy$$ Here's what I've done so far: By subtracting the second equation from the first, I got ...
0
votes
1answer
28 views

How to plot a phase portrait for system of differential equations in mathematica or R?

Please, help me. I'd like the phase portrait for this system: If anyone can make this portrait and post a print screen here, I would thank you very much.
0
votes
1answer
20 views

Gaussian elimination problem

$$x_1 + 10x_2 − 3x_3 = 8$$ $$x_1 + 10x_2 + 2x_3 = 13$$ $$x_1 + 4x_2 + 2x_3 = 7$$ when making 2nd and 3rd 1st columns 0 using Gaussian elimination, the second row second column also becomes zero, so ...
-1
votes
2answers
31 views

System differential equations 0 [on hold]

System of nonlinear differential equations $$y'= -\frac{4y}{x+4}+\frac{y^2x}{4t}, $$ $$ x'= \frac{x^2}{t^2}-\frac{9x}{t}+24 $$ help if I understood correctly you need to express $x$, but I can't
5
votes
2answers
59 views

General solution to a system of non linear equations with a specific pattern

I am seeking a general solution to a system of non linear equations with a specific pattern: Order 1: $$ x_0 = a^2 + b^2 $$ $$ x_1 = 2ab $$ Order 2: $$ x_0 = a^2 + b^2 + c^2 $$ $$ x_1 = 2ab + 2bc ...
0
votes
2answers
50 views

How do you find the value of n in this example

$$n^{n-2} = 16$$ I know $n = 4$ through trial and error but how do you find $n$ in a conventional manner? I'm basically trying to solve how many nodes are in a tree that has $16$ spanning trees ...
2
votes
1answer
8 views

Equation for sinusoidal wave with fixed wavelength and amplitude

I am a programmer. I am writing a program in which I need to show a graph plotted to the user when the user adjusts two sliders, which are the amplitude and wavelength of the wave, say...
0
votes
1answer
22 views

Difference in using mldivide and pinv in MATLAB with over-determined system and rank deficient [on hold]

I am dealing with the problem $\mathbf{Ax} = \mathbf{B}$ and my problem is over-determined problem and matrix $\mathbf{A}$ is rank deficient. As we all know we can solve this in a least square sense ...
4
votes
1answer
66 views

Knight movement on chess field

I had this task in programming competition: There are two knights, which are $(p_1,q_1)$ and $(p_2, q_2)$. $(p,q)$ knight is figure, with p(q)-length first step, and q(p)-length second step in ...
1
vote
1answer
31 views

Weird contradiction between equations

A guy that I tutor came to me with the following question: The time it takes for body $A$ to pass 160 km is 5 hours longer than the time it takes for body B to pass 90 km. The speed of body A is ...
6
votes
4answers
71 views

Prove that for any given $c_1,c_2,c_3\in \mathbb{Z}$,the equations set has integral solution.

$$ \left\{ \begin{aligned} c_1 & = a_2b_3-b_2a_3 \\ c_2 & = a_3b_1-b_3a_1 \\ c_3 & = a_1b_2-b_1a_2 \end{aligned} \right. $$ $c_1,c_2,c_3\in \mathbb{Z}$ is given,prove that $\exists ...
1
vote
2answers
28 views

Writing system of equations & rate of change

"Two planes leave a city for another city that us 600 miles away. One of the planes is flying 50 miles per hour faster than the other. The slower plane takes 2 hours longer to reach the city. What is ...
1
vote
1answer
32 views

Prove that the solutions to the system of equations are integers

Let $a, b \in \mathbb{Z}$ and consider the system of equations below: $$\begin{cases} y -2x-a =0\\ y^2-xy+x^2-b=0\end{cases} $$ Prove that $x,y\in\mathbb{Q}$ implies $x,y\in\mathbb{Z}$. I ...
2
votes
3answers
71 views

Matrix Problem of form Ax=B

The matrix $A$ is given by $$\left(\begin{array}{ccc} 1 & 2 & 3 & 4\\ 3 & 8 & 11 & 8\\ 1 & 3 & 4 & \lambda\\ \lambda & 5 & 7 & 6\end{array} \right)$$ ...
1
vote
1answer
42 views

Relatively simple system of nonlinear ODEs

There are a lot of questions like this on MSE as well as online resources on the subject, but a) the MSE questions are either unanswered or correspond to systems substantially different from this one, ...
2
votes
1answer
19 views

System of DEs with constant term

This is similar but not identical to standard examples in e.g. Paul's Notes, and while the math seems straightforward the results I get disagree with what I get from numerical simulation. Given a 2D ...
0
votes
0answers
14 views

show that $y$ and $x$ can be expressed as a function of $x$ alone in the neighbourhood of the point $(2,1,-1)$

Let $$f(x,y,z)=[x^2-2xz+y^2z^3-7,2xy^4-3y^2+xz^2+5z+2]=(0,0)$$ at $$(2,1,-1)$$ The only method that I have known is the one for solving the homogenous system say for $y$ and $z$ in terms of $x$ but ...
0
votes
2answers
23 views

Existence if integer solutions

How many integer solutions exist for: \begin{cases} x+y=1-z \\ x^3+y^3=1-z^2 \end{cases} How do I do this. I'm stuck
1
vote
3answers
43 views

Consider the parametric curve: $x=6\cos^3(t), y=6\sin^3(t)$, write it in cartesian form.

Consider the parametric curve: $$x=6\cos^3(t), y=6\sin^3(t)$$ Write it in Cartesian form. I am really struggling with the solution for this. I've been trying to find $t$ from $x$, and then ...
1
vote
2answers
58 views

How to show whether 3 planes have a common line of intersection

To show whether or not the 3 planes $$x+y-2z=5\tag 1$$ $$x-y+3z=6 \tag2$$ $$x+5y-12z=12 \tag 3$$ all have a common line of intersection. Can I do $(3)-(2)$ to get the line $6y-15z=6$ and $(1)-(2)$ ...
1
vote
2answers
17 views

Special method of solution for $A\vec x=\vec b$ where $A$ is a square matrix such that $A^tA$ is diagonal and has full rank?

Is there any special shorter method of solution other than cramer's rule for solving a system of $n$ linear equations in $n$ unknowns $A\vec x=\vec b$ where the square matrix $A$ has the property that ...
0
votes
1answer
12 views

Can we ensure convergence for the jacobi method or do we simply trial and error?

For iterative methods for solving systems of equations, we may not always get convergence and it can depend simply on the way in which we write the equations. I understand there are tests which will ...
0
votes
1answer
18 views

Need to find 3 unkown variables

In the city is $3$ types of hotels. In the $I$ type there is $150$ basic apartments and $17$ luxury apartments, in the $II$ type $310$ - basic and $37$ - luxury and in the last $III$ type $40$ - basic ...
0
votes
0answers
36 views

can it be solved without vieta formulae ??

recently i came across an anonymously remarkable algebra question which is as follows If the polynomial $$F(x)= 4x^4 - ax^3 + bx^2 - cx + 5$$ where $a,b,c$ belongs to $\mathbb R$ has 4 positive real ...
1
vote
3answers
58 views

For which values does the Matrix system have a unique solution, infinitely many solutions and no solution?

Given the system: $$\begin{align} & x+3y-3z=4 \\ & y+2z=a \\ & 2x+5y+(a^2-9)z=9 \end{align}$$ For which values of a (if any) does the system have a unique solution, infinitely many ...
0
votes
2answers
33 views

Linear Hamiltonian System

Suppose the linear system: $\dot{z} = J \frac{\partial{H}}{\partial{z}} = J S(t) z = A(t) z$, with Hamiltonian $H=H(t,z)=\frac{1}{2} z^T S(t)z$. How can I prove that: $$\frac{d}{dt}H(t,\xi(t)) = ...
1
vote
2answers
33 views

Finding answers to system of equations

Let's say we have such a system structure of equations: ...
1
vote
3answers
43 views

Systems of equations problem in algebra

A dog weighs 1/8 of a cow. Their combined total is 360kg, how much does the dog weigh and how much does the cow weigh? I got this question on my algebra test, my teacher said the answer was along ...
0
votes
1answer
39 views

Could someone explain how to solve these sets of equations please?

I am given that; $$x_1 + x_2 + x_3 = 75$$ $$x_1 + x_2 + x_4 = 75$$ $$x_1 + x_3 + x_4 = 75$$ $$x_2 + x_3 + x_4 = 75$$ I need to find $x_1, x_2, x_3$ and $x_4$. I know that each variable equals 25. ...
1
vote
0answers
21 views

How to find value of an unknown in matrix to make system of linear equations consistent

I'm currently stuck on this question relating to finding the unknown in a matrix so that the system of linear equations is consistent. I need to solve for $\lambda$. My first instinct is to try and ...
0
votes
2answers
94 views

Solutions for $-x=\textrm{tan}(x)$

How can the following equation be solved? $-x=\frac{\sin(x)}{\cos(x)}$, $x \in \mathbb{R}$ I understand $x=0$ is one solution, but I need all of them (In particular, precisely those that are not ...
0
votes
0answers
17 views

System of linear equations with repeated equations

Suppose that I have this over-determined system of equations, $$a_1x_1 + a_2x_2 + a_3x_3 = k_1$$ $$b_1x_1 + b_2x_2 + b_3x_3 = k_2$$ $$c_1x_1 + c_2x_2 + c_3x_3 = k_3$$ $$d_1x_1 + d_2x_2 + d_3x_3 = ...
2
votes
1answer
32 views

Building a Diet Using Linear Algebra

The Question Suppose a diet calls for 7 units of fats, 9 units of protein and 16 units of carbohydrates for the main meal. Suppose the dieter has 3 possible types of food to satisfy this requirement: ...
0
votes
0answers
23 views

Numerical scheme for system of PDEs

I'm trying to solve the following coupled PDE system for my master thesis: \begin{align} \kappa_0\frac{\partial p}{\partial t}&=- \nabla \cdot v \\ \rho_0\frac{\partial v }{\partial t} &= ...
2
votes
2answers
55 views

Find numbers $a, b, c$ given that $a+b+c=12$, $a^2+b^2+c^2=50$, and $a^3+b^3+c^3=168$

Let $a+b+c=12$, $a^2+b^2+c^2=50$, and $a^3+b^3+c^3=168$. Find $a,b,c$ Suppose $a, b, c$ are roots of $P(x)$. $$P(x) = k(x - a)(x - b)(x - c)$$ But then I get $(k = 1)$ $$P(x) = x^3 - 12x^2 + ...
6
votes
6answers
81 views

System of equations involving sin and cos

I'm trying to solve the following system: $$ \sin(x) + \cos(y) = 0.6\\ \cos(x) - \sin(y) = 0.2\\ $$ Solving for y in terms of x: $$ y=\arccos(0.6-\sin(x))=\arcsin(\cos(x) -0.2) $$ Therefore: $$ ...
0
votes
1answer
43 views

How to solve congruence modulo equations?

While studying Affine Cipher in cryptography it tells that we need to solve a system of modulo congruence equations. The equations are: $8\alpha+\beta\equiv 15 \pmod{26}$ $5\alpha+\beta\equiv 16 ...
0
votes
1answer
14 views

solving system of two equations

I understand up until the "this system gives" Where did he get the $u = 2v = 2(2u)=...$ line from? Also note that $k \not= 0 $here