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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1
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0answers
27 views

How to find a linear equation with the same solution set?

I have this homework question that I solved, but it was so easy that I feel like I did something wrong. Can someone just confirm that my approach to this problem was correct? So, I have to find a ...
1
vote
1answer
30 views

How can I solve this set of linear coupled system?

Consider the matrix $A=\begin{bmatrix} -2k & k \\ k & -2k \end{bmatrix}$ .I have to solve this linear coupled system : $X'' = A.X$, where $X= \begin{bmatrix} x_1(t) \\ x_2(t) \end{bmatrix}$ ...
1
vote
1answer
23 views

Using jacobian to solve a nonlinear system of equations?

I have to solve a system of nonlinear equations using jacobian but I'm not sure how to solve for the solutions. I remember one of my friends doing $Ax = B$; where jacobian matrix was $A$, but im not ...
0
votes
4answers
43 views

Physics problem, stuck in algebra.

I end up with the equations; $$u=u_1' \cos(a)+u_2' \cos(b)$$ $$u_1' \sin(a)=u_2' \sin(b)$$ $$u^2=u_1'^2+u_2'^2$$ I have to show that $$a+b=\frac{\pi}{2}$$ $x'$ isn't the derivative of $x$, it's a ...
0
votes
0answers
28 views

Avoiding initial guess in Newton Method for nonlinear systems

Peace be upon you, I am solving the following system of equations for finding $\gamma$ and $\theta$, while I have about 18000 pairs of $\{c1,c2\}$ constants (i.e. I have about 18000 of such systems ...
2
votes
4answers
84 views

Solution to a system of nonlinear equations

Do you know any method to solve the following system of nonlinear equations ? $\begin{equation} 141,3829=A+\frac{B}{323}+5,78C+F323^{E}\\ 69,07645=A+\frac{B}{333}+5,81C+F333^{E}\\ ...
-2
votes
2answers
25 views

System of linear equation matrix? [duplicate]

How would I do this question. Determine the value(s) of $h$ such that the matrix is augmented of a consistent linear system. My matrix \begin{bmatrix} 1&h&4\\ 3&6&8 \end{bmatrix} I ...
0
votes
3answers
51 views

Horse Betting Odds - But Guaranteed Win!

Suppose four horses - $A, B, C$, and $D$ - are entered in a race and the odds on them, respectively, are $6$ to $1$, $5$ to $1$, $4$ to $1$, and $3$ to $1.$ If you bet $\$1$ on $A$, then you receive ...
0
votes
1answer
46 views

Solving system of equations with complex numbers

Equation 1$$ \frac{V_{1}}{5} + \frac{V_{1}-V_{2}}{10+j6} - 10\angle45^\circ = 0 $$ Equation 2 $$ -4V_{1} + \frac{V_{2}-V_{1}}{10+j6} + \frac{V_{3}}{-j2} + \frac{V_{3}}{8+j7} = 0 $$ Equation 3 $$ ...
0
votes
3answers
56 views

System of linear equation

Determine the value for k for which the system of linear equation has infinitely many solution. \begin{cases} 2x - y = 2\\ 4x + ky = 4 \end{cases}
1
vote
0answers
53 views

Find the fundamental matrix of a system of ODEs?

To linearize a system, in one of the steps I am required to find the fundamental matrix $\Phi$(t) of a system such that $\Phi$(0)=I. The example system my professor used: $\dot{x} = x - y - x^3 - ...
3
votes
0answers
22 views

Algorithms for solving overdetermined, homogeneous linear systems with multivariate polynomial coefficients

I would like to solve overdetermined, homogeneous linear systems of equations with multivariate polynomial coefficients, i.e., $Ap=0$ with $A$ an $m\times n$ matrix, $m\gg n$, and $a_{i,j} \in ...
2
votes
0answers
25 views

Solving a system of first order differential equations

So, I have (another) problem with differential equations (from an optimal control problem). I am trying to solve the following system of DEs (is this even a system?): $$ \lambda'(t) = r \lambda(t) + ...
2
votes
5answers
71 views

Algebraic process to find numbers so that $xy=45$ and $x+y=18$

Can someone help me with the following question? The sum of two numbers is $18$ and their product is $45$. Find the numbers. I know that the answer is $15$ and $3$. But how do I find that answer ...
0
votes
1answer
32 views

Mathematica Output Meaning ({{}}) [closed]

What does an output of {{}} mean in mathematica after solving a system? Best Regards
-7
votes
0answers
47 views

Solving a system of polynomial equations in three variables (x^2-yz=18, y^2-zx=8, z^2-xy=-7)

Solving a system of polynomial equations in three variables (x^2-yz=18, y^2-zx=8, z^2-xy=-7 I've tried rearranging each equation to isolate for one variable ex: z^2-xy=-7 --> z= x^2-18/y after, I ...
1
vote
3answers
32 views

Techniques for solving coupled differential equations

I am trying to solve a system of coupled differential equations to plot streamlines using Matlab. The equations are these: $$\frac{\mathrm{d}x}{\mathrm{d}t} = -3x - 5y$$ ...
-1
votes
2answers
22 views

Systems of equations with multiplication [closed]

If $M \times E = 6$; $N \times S = 20$; $E \times S = 15$; $E \times N = 12$; $S\times A = 30$; Then $M \times E\times N\times S\times A =$ ?
0
votes
1answer
28 views

Trying to calculate 5 simultanious equations in Mathematica

$\def\1{x_1}\def\2{x_2}\def\3{x_3}\def\f{f(\1,\2,\3)}\def\bs{\bigskip}\def\b{\begin{pmatrix}}\def\e{ ...
3
votes
2answers
88 views

Find the number of escalator steps from the number of steps made by people walking on it

Renata walks down an escalator that moves up and counts $150$ steps. Her sister Fernanda climbs the same escalator and counts $75$ steps. If the speed of Renata (in steps per time unit) is three times ...
0
votes
0answers
33 views

Solving system of equations in rationals

Do there exist solutions to solve system of $n-2$ equations with $n-2$ variables where $n$ is fixed even integer and $a_i,b,c\in\mathbb{Q},i\in\{0,1,2,\cdots,n-5\}$ $$\left\{ ...
-1
votes
1answer
19 views

Finding the value of a variable present in two functions

I have two functions each containing a variable besides an $x$. $$kx-3\quad \text{ and }\quad x^2+k$$ I set them equal to each other, but my algebra is failing me and I can't remember how to solve ...
2
votes
1answer
34 views

How to solve the system of equations $y= 5x^2-2x$ and $y=10x+9 $?

I am trying to solve this system of equations $y= 5x^2-2x$ and $y=10x+9$. I have worked the problem out and I am lost could someone please explain it? I have a test tomorrow over this information.
1
vote
1answer
42 views

Constrained Newton-Raphson method

Peace be upon you, I want to solve a system of two equations in which the existence of $ln\left(\frac{\alpha}{\alpha+\beta}\right)$ function makes some limitations in iterations of the Newton-Raphson ...
2
votes
2answers
47 views

RL circuit as a system of first-order ODEs

The system is as follows:\begin{align}i_1&=i_2+i_3,\\50\sin t&=6i_1+i_2'+5i_2,\\50\sin t&=6i_1+i_3',\end{align} I have to find $i_2,i_3$. This is my first circuit I'm trying to solve, but ...
1
vote
5answers
82 views

Arithmetic Mean, Geometric Mean, Harmonic Mean and their relations

If $a$ be the arithmetic mean between $b$ and $c$, $b$ be the geometric mean between $c$ and $a$ then prove that $c$ is the harmonic mean between $a$ and $b$. I expressed $a$ as $$a=\frac{(b+c)}{2}$$ ...
2
votes
0answers
32 views

What is the (currently) optimal root finding algorithm for multivariate functions? [closed]

Let's say we wish to find the roots of the function: $f(x,y,\cdots) = 0 \;,$ so, for a minimal example: $xy - 1 = 0 \; .$ I know there are different methods to solve this problem for the ...
0
votes
1answer
65 views

Is there any simple analytic method for solving $\sqrt{x}+y=7$ and $x+\sqrt{y}=11$ simultaneously. [duplicate]

I am thinking of a nice and simple analytic method to solve the following equations simultaneously: $$\sqrt x+y=7;\\x+\sqrt y=11.$$ To my suprise I can't. But, I solve the system numerically using ...
0
votes
2answers
26 views

Initial value problem with a delta term

Im having trouble solving this initial value problem. I know how to solve it without the delta-term (C1*e^(lambda*t)*S1 + C2*e^(lambda*t)*S2), but how do i solve it with a delta term?
0
votes
2answers
39 views

Substitution vs Elimination in Solving Systems of Equations

When solving systems of equations, is it more efficient in terms of time to solve it using substitution or elimination, and what are your reasons for saying so?
12
votes
2answers
636 views

System of non-linear equations.

I have to find all triplets $(x,y,z)$ that satisfy: $$x^{2012} + y^{2012} + z^{2012} = 3\\x^{2013} + y^{2013} + z^{2013} = 3\\x^{2014} + y^{2014} + z^{2014} = 3$$ I've found the trivial solution ...
0
votes
0answers
19 views

Problem of choice under conditions of certainty and with immediate effect.

A transport company expects to deliver 8,000 tons of goods per month for six months, 6000 tons per month for three months, 5000 tons in July, 5000 tons in August, and 4000 tons in January. Each truck ...
3
votes
2answers
79 views

Find all complex number $z\in\Bbb{C}$ such that $\vert z\vert=\vert z^{-1}\vert=\vert z-1\vert$

Find all complex number $z\in\Bbb{C}$ such that $$\vert z\vert=\vert z^{-1}\vert=\vert z-1\vert$$ I tried to write $z=a+ib$, clearly $z=1$ is not a solution. I have to solve $$\left\{ ...
0
votes
1answer
27 views

Transformation of inverse to a system of linear equations

I have $X = (U'WU)^{-1}U'$ to be solved. Suppose $U'$ is $3 \times 7, W$ is $7 \times 7$ positive definite matrix, $U'$ is of rank 3. So, I transformed $(U'WU)^{-1}U'$ as $(U'WU)^{-1}U'WU = I\\ XWU ...
0
votes
3answers
45 views

Is there anyway to find the values for equation with two variables

Is there mathematical anyway to find the values for equation with two variables? as example: I have y = (20x+3)r+x and y is 50. then what is x and r values?
0
votes
2answers
47 views

How can I find the R values

I have the following equations : $$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N= R - S \end{cases}$$ - And I have the $B$ values, e.g : 834343, 3253538, ...
3
votes
2answers
55 views

Can a straight line be drawn from origin to co-ordinate X,Y?

Given a co-ordinate P(X,Y), can a straight line be drawn from origin to P, if there is wall existing with end points A(X1,Y1) and B(X2,Y2)? My Approach: I first of all wrote the equations from origin ...
0
votes
1answer
59 views

how can I find equation variables?

I have the following equations : $$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N=S-R \end{cases}$$ - And I have the $B$ values, e.g : 173, 283, 2343, 834343 ...
4
votes
4answers
499 views

What is the non-trivial, general solution of these equal ratios? [closed]

Provide non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ $a=?, b=?, c=?$ The solution should be general.
0
votes
0answers
11 views

unknown function: calculation of coefficients in series expansion up to a given degree

I am trying to solve an functional equation of unknown $h\mapsto h(x)$ ($x\in\mathbb{R}$, in the neighbourhood of $0$): $$\mathcal{F}(h)=\mathcal{G}(h) \qquad (*)$$ (assume $\mathcal{F}$ and ...
1
vote
0answers
19 views

Verification - Matrices and Linear Equations Part 1

Would just like to verify my Answers and bounce off my ideas and thinking with someone as I feel quite alone in this course. I am usually great at maths and enjoy it but these matrices and linear ...
1
vote
1answer
35 views

Solution to two equations with three unknowns

So I'm a student studying through correspondence and I need some help. This is an assignment question, and I have tried everything I know how, to answer it which has lead me to the conclusion that ...
1
vote
2answers
227 views

Matrix Equation- solution

Sir, We have given $A= \begin{bmatrix}q_1 & q_2&q_3 \\ q_4 & q_5&q_6\\ q_7 & q_8&q_9 \end{bmatrix} \tag 1$. A is a matrix with determinant 1,orthogonal , invertible and ...
0
votes
4answers
64 views

How to solve these simultaneous equations using any better way?

This problem is easy, but I am just curious whether there is any better and more elegant method of solving. Solve the simultaneous equations: $$2x^2+5xy+2y^2=0,$$ $$x^2-y^2=1.$$ The way I solve it ...
0
votes
1answer
50 views

Finding the fixed points of a recurrence relation (and systems of) analytically?

How would I go about finding the fixed points of the following recurrence? $$X_n = 2X_{n-1}(2- 3X_{n-1}) + X_{n-1}$$ And therein, determining their stability analytically? Also, how does one find ...
3
votes
2answers
39 views

Solving $4y^4 - 4x^4 + x + y = 0$ (equation system of partial derivates)

I need help solving the following equation system: $$ \frac{\partial}{\partial x} = 8xy + 4y^2 + \frac{y}{x^2 + y^2} = 0 $$ $$ \frac{\partial}{\partial y} = 8xy + 4x^2 - \frac{x}{x^2 + y^2} = 0 $$ ...
2
votes
0answers
30 views

Method of characteristics for systems of PDE (vs. Lewy's example)

Main question: How does the method of characteristics generalize for systems of first order PDE, as opposed to scalar PDE? Namely, is there such a generalization at all, and if so what information ...
0
votes
1answer
44 views

How to solve a nonlinear system of three equations involving rational functions?

How do I get $a$, $b$, and $c$? Given $$X=\frac{a+\frac{1}2b}{a+b+c}$$ $$Y=\frac{b(\frac{\sqrt3}{2})}{a+b+c}$$ $$Z=\frac{76a+150b+29c}{255}$$ in other words How do i get $a$, $b$, and $c$ on the ...
0
votes
2answers
41 views

How to solve the system $ax>y+z$, $by>x+z$, $cz>x+y$ in positive numbers?

Let $a>b>c>1$. How to find solutions in positive numbers of the following system? \begin{cases} ax>y+z \\ by>x+z \\ cz>x+y \end{cases}
0
votes
1answer
25 views

How to find parameters that minimize the sum of squares, using Matlab?

I have a system of linear equations in the following form. How can I solve it in Matlab? $$\operatorname*{argmin}_{a,b} \sum_{i,j} [X(i,j)-a\times Y(i,j)-b]^2$$ Where X and Y are known. I need to ...