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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46 views

What is the solution of this system of equations?

Lat $(a,b,c)\in S^2$, where $S^2:=\{(x_1,x_2,x_3)\in \mathbb R^3: x_1^2+x_2^2+x_3^2=1 \}$. How to solve the following system of equations: $$ x^2+y^2-z^2-t^2=a,\\ 2(yz+xt)=b,\\ 2(yt-xz)=c,\\ ...
2
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1answer
16 views

For a linear system, why is direction “stored” in the variables when considering it as linear equations, but in vectors when its as a vector equation?

Given an arbitrary system of equations, why is direction in space "stored" in the variables when considering the system as linear equations, but "stored" in vectors when considering the system as a ...
2
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1answer
22 views

System of vector equations (in Minkowski space)

I wonder whether there is a systematic approach to find (or at least whether there are criteria for the existence of) vectors $P_0, P_1, \dots, P_n$, say in $n$-dimensional Minkowski space of ...
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3answers
52 views

How many of each ticket were sold in one day? [on hold]

Child tickets - $\$7$ Adult Tickets - $\$10$ Senior Tickets - $\$5$ Day one sold $678$ tickets for $\$5,812$ Day two sold $535$ tickets for $\$4,541$ How many of each ticket were sold on day one ...
4
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1answer
53 views
+50

Pentagonal Numbers

I recently was passing some time on Project Euler, when I came across this question. It deals with finding Pentagonal Numbers $P_j$ and $P_k$ such that $P_j+P_k$ and $P_j-P_k$ are also pentagonal ...
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3answers
44 views

A jazz concert brought in 128,000 on the sale of 8,100 tickets. If the tickets sold for $10 and $20 each, how many of each type ticket were sold? [on hold]

I am currently struggling on how to figure this out. I got as far as 165,000-81,000=84000. I am unsure what to do next. Thank you in advance!
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2answers
32 views

Solutions to Linear Equation

I have these two equations: $cx+y=5, x+y=2$. For what $c$ would this have no solution, infinite solution, unique solution. For no solution I got when c=1, and for c=0, we have unique solution. Is ...
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2answers
24 views

questions about systems of equations using matrices and row echleon

I have the following matrix: $$ \left[ \begin{array}{cc|c} -1&-2&{\sqrt 2}\\ -8&2&{\sqrt 3} \end{array} \right] $$ So the first thing I do is multiply R1 by - 1 to ...
3
votes
1answer
64 views

A symmetric system of nonlinear equations - how to solve?

So, I was adviced to ask a new question on my problem (as the first one wasn't very precise), that is to solve the system of equations: $$\begin{cases} x\cdot y=6 \\ x^y+y^x=17 \end{cases}$$ where: ...
1
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2answers
33 views

systems of equations with 3 variables - addion method

I am stuck on solving the following systems of equations with 3 variables. The textbook asks to use the addition method so can we please stick to that. ${5x -y = 3}$ ${3x + z = 11}$ ${y - 2z = ...
0
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1answer
30 views

systems of equations with 3 variables using substitution method

I am struggling to solve the following system of equation with 3 variables. The textbook asks to use the substitution method so I would appreciate answers that use that. I have the following 3 ...
0
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1answer
20 views

simultaneous equations with 3 variables

I have the following 3 equations and I need to find out if they are consistent, inconsistent or dependent using the substitute method. I am using a textbook that wants you to use the substitution ...
2
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4answers
34 views

simultaneous equation using the substitute method

I have the following 2 equations: ${6x + 9y = 3}$ ${6x -3y = -2}$ The textbook asks to use the substitution method so I would appreciate if we stuck to this method, I could use the addition method ...
0
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0answers
6 views

How to find $B$ by solving the following linear system: $s_k$ $B$ ${s_k}^T$ $=1,$

How to find $B$ by solving the following linear system: $s_k$ $B$ ${s_k}^T$ $=1,$ $\qquad$ for $k=1 ... ,p$. Where $s_k$ is a $1\times3$ row_vector from the matrix $S= [s_1 ... ...
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0answers
25 views

Solve the system of trigonometric equetions, inverse kinematics

I am trying to do inverse kinematics for some mechanical system. After applying Neton-Euler method following equations were obtained: $$F_x = k_f w_l\sin(\beta_l) + k_f w_r\sin(\beta_r)$$ $$F_y = k_f ...
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0answers
5 views

Error bounds for solution of system of linear equations when coefficients are uncertain

I have a square system $Ax=b$ and would like to know how much the solution $x$ can change when I change the coefficient matrix $A$. I've stumbled upon the condition number, but this seems to apply ...
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0answers
86 views

Blowing-up a singular point

I have this system of ODEs: $$x'=-y+ \mu x(x^2+y^2)$$ $$y'=x+ \mu y(x^2+y^2)$$ I already find that in $\mathbb{R}^2$ the only singular point is $(0,0)$. So I have to blow-up the singularity to find ...
0
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1answer
22 views

Rotated parabola 2d vertex

I'm implementing an application where I need to get the vertex of a parabola, the parabola might be tilted; so it can have an angle with the x-axis not necessarily vertical or horizontal. Can I get ...
0
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0answers
10 views

How to rescale parameters?

First of all, I am a maths newby and never got any education on rescaling parameters on whatsoever. The knowledge that I have is based on what I know from mathematical research papers and as ...
2
votes
1answer
67 views

Find quickest line of interception to a moving object

First, a visual illustration of the problem: http://tube.geogebra.org/m/1512793 The goal is to mathematically predict the direction in which the player need to run to intercept the ball as fast as ...
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0answers
7 views

Equation system with random variables

Suppose we have such system: Xt1+Ym1+Zp1+r1 = Xt2+Ym2+Zp2+r2 = Xt3+Ym3+Zp3+r3 = Xt4+Ym4+Zp4+r4 = ... (and more) where t[i], m[i], p[i] - are known variables; r[i] - are minor unknown random numbers ...
3
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4answers
19 views

An equation to represent all vector solutions to a system of equations with infinite solutions

If both $x$ and $y$ are solutions to a system of linear equations with infinite solutions then $$z = αx + (1 −α)y$$ is also a solution for any real α. I'm having some trouble understanding this. ...
2
votes
3answers
57 views

Solving a system of two equations

I have a system of equations: $$ \begin{cases} x\cdot y=6 \\ x^y+y^x=17 \end{cases} $$ I was able to guess that the pair $2,3$ satisfies the system, but my question is: how to solve such system of ...
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4answers
46 views

The set of real values of $x$ satisfying the equation $\left[\frac{3}{x}\right]+\left[\frac{4}{x}\right]=5$

The set of real values of $x$ satisfying the equation $\left[\frac{3}{x}\right]+\left[\frac{4}{x}\right]=5$,(where $[]$ denotes the greatest integer function) belongs to the interval ...
0
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3answers
56 views

Solving linear system of equations to obtain different classes of solution.

Correct me if I am wrong. Find the value(s) of the constant $k$ such that the system of linear equations $$\left\{\begin{array}{l} x + 2y = 1\\[2ex] k^2x − 2ky = k + 2 \end{array} \right.$$ has: ...
4
votes
1answer
845 views

How to solve coupled linear 1st order PDE

It is fairly straight forward to solve linear 1st order PDEs by the method of characteristics. For example, if $\partial_tf+a\partial_xf=bf$ , we have that $\dfrac{df}{dt}=bf$ on the characteristic ...
9
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5answers
547 views

How to solve an exponential and logarithmic system of equations?

$$ \left\{\begin{array}{c} e^{2x} + e^y = 800 \\ 3\ln(x) + \ln(y) = 5 \end{array}\right.$$ I understand how to solve system of equations, logarithmic rules, and the fact that $\ln(e^x) = e^{\ln(x)} ...
0
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0answers
29 views

How can I solve the system of equation with 2 quadratic equations and 3 linear equations?

Let $k>1$ be an integer and let $x_1,x_2,y_1,y_2,z_1$ and $z_2$ be the unknowns. How can I solve for the unknowns given the following equations? ...
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0answers
18 views

Systems of Linear Equations- number of solutions [closed]

What exactly is a rigorous proof that: A) if there are the same number of variables as equations- there is exactly one solution B)if there are less variables than equations then there is either one ...
2
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0answers
27 views

Inverting an isometric projection?

I'm trying to invert a function that takes points on a 2-d plane to an isometric projection of that plane. This function is encoded as follows (as part of the Isomer library): ...
0
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2answers
25 views

Solving a system of polynomial equations

How can I solve a system of polynomial equations like this one Maybe I'm missing a very basic trick... Can anybody suggest me an approach?
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0answers
18 views

Help for solving this optimization problem

Are given $2$ square matrices $M_1$ and $M_2$ of dimension $d \times d$ and two points in a $d$-dimensional space $p_1$ and $p_2$ ($d \times 1$). Now I need to find two other square matrices $X$ and ...
0
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0answers
8 views

Which one will be better in Crout v/s Dolittle decomposition?

I recently read about the Cholesky , Crout and Dolittle decomposition. However, after studying Dolittle , I was wondering why is there a need for Crout decomposition to exist. I mean what upper hand ...
2
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3answers
54 views

Nonlinear system Diophantus.

In the extant books of Diophantus, are considered in the system of equations. Of interest is the non-linear system of Diophantine equations. Some simple systems from his book manages to solve it. ...
1
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1answer
364 views

solving a non-linear (trigonometric) system of equations with two equations and two variables

I'm trying to solve the following system of equations: $$l_1*sin(\alpha)=l_2*cos(\gamma)+l_3*sin(\beta)$$ $$l_2*sin(\gamma)+l_1*cos(\alpha)=l_3*cos(\beta)+l_4$$ with the unknowns $\beta$, $\gamma$ ...
0
votes
2answers
60 views

Maxima not finding solution to simultaneous equations when one exists

I am using Maxima to solve the following equations simultaneously: $$ 990=e^x \tag{1}$$ $$ 590=e^{(x - 10y)} \tag{2}$$ however the command ...
0
votes
2answers
61 views

solving a system of equations (3 equations, 3 variables)

I have 3 equations and 3 unknown variables as follows $$\frac{\beta}{1-\alpha}x=y^{\alpha-1}-z$$ $$\left(1+\frac{\beta}{1-\alpha}\right)x=\frac{1}{\sigma}\left(\alpha y-\rho\right)$$ ...
0
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2answers
34 views

Does this system of linear equations have infinite solutions?

$$x(k+2)+y(k−1)+z(k)=2$$ $$y(k+2)+2z=0$$ $$z(k^2+k−2)=k+2$$ Is there any value of k for which this system of linear equations would have infinite solutions? I mean, it seems as if it does when k = ...
2
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1answer
47 views

Solving a System of Linear Equations (k value for infinite, unique and no solutions)

$$x(k+2) + y(k-1) + z(k) = 2$$ $$y(k+2) + 2z(k) = 0$$ $$ z(k^2 + k -2) = k + 2$$ Determine the values of k for which the system has: Exactly one ...
2
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0answers
38 views

Solving $-1=e^a-2e^{av}$ as part of a equation system

Problem Given $f_2(x)=e^{ax-b}+c$ with $x \in \left(0,1\right)$, I am trying to calculate the parameters $a,b,c$ in respect to the following constraints: $$ \begin{align} f_2(0) &= 0 \\ ...
4
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1answer
43 views

Slightly different results to an ODE system - hand calculation vs Mathematica

This has been driving me mad for the last few days. I have a a pair of ODEs: $$\frac{d^2 M_N}{d x^2}=\lambda_{N}^2 M_N$$ $$\frac{d^2 M_{N-1}}{d x^2}=\lambda_{N-1}^2 M_{N-1}-\frac{f}{d_{N-1}}M_N$$ ...
4
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2answers
57 views

Prove that system of equation implies statement

How to prove that $$ \begin{cases} x_1 + x_2 + x_3 & = 0 \\ x_1x_2 + x_2x_3 + x_3x_1 & = p \\ x_1x_2x_3 & = -q \\ x_1 & = 1/x_2 + 1/x_3 \end{cases} $$ implies $$ q^3 + pq + q = ...
0
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0answers
30 views

Equation with a summation (Use of Harmonic series)

I have a sum $\sum\limits_{i=j}^k \dfrac{1}{i^s}$ and a constant $j$. I would like to determine $k$ such that $\sum\limits_{i=j}^k \dfrac{1}{i^s}=C$ where $C$ is a constant $< 2$. How can I ...
1
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1answer
29 views

Number of solutions in system of linear equations

I'm studying System of linear equations. When solving Ax=b, it is said that the system can behave in 3 ways. No solution Unique solution Infinitely many ...
3
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1answer
100 views

Need help with this proof, I don't understand it , could anyone clarify some of the details. System of linear Differential equations.

$$(*)X'=A(t)X - system$$ $$(*)PX(\alpha)+QX(\beta)=0.$$-border conditions, where P,Q constant square matrices $n \times n $. Let $Y(t)$ be the fundamental matrix for the system $(*)$ normed for$ t= ...
1
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1answer
34 views

Finding values of $a$ with which a simple system has exactly 2 solutions

The problem is: Find such values of $a$ with which the system will have exactly two solutions I understand the solution provided at the Resuhege.ru website (problem no. 484630): First ...
3
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2answers
1k views

On a linear $3\times 3$ system of differential equations with repeated eigenvalues.

I have the following system: $$\begin{cases} x'= 2x + 2y -3z \\ y' = 5x + 1y -5z \\ z' = -3x + 4y \end{cases} $$ $$\det(A - \lambda I)= -(\lambda - 1)^3$$ the eigenvector for my single eigenvalue ...
1
vote
1answer
47 views

Solve the equation: $(9x^2+6x-8)\sqrt{3x+2}+6x+23=27x^2+3\sqrt{10+3x}$

Solve the equation: $(9x^2+6x-8)\sqrt{3x+2}+6x+23=27x^2+3\sqrt{10+3x}$ I used wolframalpha.com and got only solution $x=-\dfrac{1}{3}$. And this is my try: Condition: $x\ge-\dfrac{2}{3}$. ...
0
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0answers
40 views

Simplifying and solving system integral equations

I want to solve the following system of equations: First equation $\int_0^\infty \!$ $\bigg[$ $\alpha y (1-r)$ $\frac{e^{-rty}}{e^{-rty} + \frac{1}{q_0} - 1}$ $\bigg]$ $e^{-pt}$ dt - ...
1
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0answers
44 views

Solving quadratic congruences

System of equation is : $$ x^2 \equiv 2 \mod 3 $$ $$ x^2 \equiv 4 \mod 5 $$ So, if first equation doesn't have solution what should I do with it?