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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2
votes
1answer
16 views

How to find the minimum sum of unknown variables that is a solution to a system of two linear equations?

I'm trying find the minimum sum of $x_{1} + x_{2} + ... + x_{n}$ where these are a solution to a linear system of two equations. System of linear equations in general form: $$ a_{11}x_{1} + ...
2
votes
1answer
43 views

How to solve these equations?

How to solve these equations for a, b, c and x? I have the following: $ 2a+b+c = 1$ $a = (a+b)x + 0.25(a+c) $ $a=(a+c)(1-x)$ $b=a(1-x)+c(x-0.25)$ $c=b(1-x)+a(x-0.25)$ I tried, but ended ...
0
votes
1answer
23 views

Dice game and points [on hold]

A dice game is played and when a round is won the player earns 9 points and when a round is lost, a player loses 4 points. After 15 rounds a player has 18 points, how many rounds did that player ...
2
votes
3answers
24 views

Considering Units When manipulating system of Equations?

I few days ago I solved a problem on a website called brilliant.org, I can not seem to find the problem there anymore but I still remember it: Q: You go to a candy store to buy m&ms and ...
2
votes
1answer
19 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
votes
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 ...
0
votes
1answer
47 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,\\ ...
-3
votes
3answers
46 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!
0
votes
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 ...
1
vote
2answers
25 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 ...
0
votes
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 ... ...
0
votes
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 ...
0
votes
0answers
26 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 ...
4
votes
2answers
83 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 ...
0
votes
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
votes
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 ...
0
votes
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
votes
4answers
20 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. ...
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: ...
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 ...
1
vote
4answers
48 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
votes
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: ...
0
votes
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? ...
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 ...
1
vote
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
votes
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 ...
9
votes
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
votes
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
votes
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
votes
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
votes
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?
0
votes
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
votes
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
votes
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 ...
4
votes
1answer
45 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: $$\frac{d^2 M_N}{d x^2}=\lambda_{N}^2 M_N$$ $$\frac{d^2 M_{N-1}}{d x^2}=\lambda_{N-1}^2 M_{N-1}-\frac{f}{d_{N-1}}M_N$$ ...
2
votes
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 \\ ...
2
votes
3answers
55 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. ...
0
votes
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
vote
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 ...
0
votes
2answers
61 views

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

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

System of differential equations - find two solutions

Here is my task: Find two solutions of system of equations: $y'=y+3z$ $z'=y-z$, Check (using the Wronskian) if the solutions are linearly independent. Then write a general solution, and then find ...
-1
votes
2answers
22 views

System of equations help

How do you get $a=2$ and $d=5$ from the two equations (see where I marked it)? Thank you!
0
votes
1answer
35 views

What is the error made in this strategy for solving linear equations?

The solution to the system $4y=3x+7$ and $9x+4y-139=0$ is shown below. I solved for the solution and found that the answer is correct, and is $(11, 10)$. But, what is the mistake that is made here? ...
0
votes
0answers
40 views

How to divide a distance with tricky proportions

I have to divide a distance between two points (A, B), with specified proportions. Equations: $d_1 + d_2 = D$ $P_a * Log[\frac{4\pi d_1}{\lambda}] = P_b * Log[\frac{4\pi d_2}{\lambda}]$ $D, P_a, ...
1
vote
0answers
32 views

ODE system, find initial conditions

I am trying to solve this problem: Given the system $$x_1'=-x_2$$$$x_2'=2x_1+3x_2$$ Find the general solution and the set of initial conditions such that the solution tends to $0$ when $t$ tends to ...
0
votes
1answer
22 views

Gaussian Elimination General Solution

Find the general solution of the following system of equations: Using Gaussian Elimination I was able to get the following solutions for these equations: x = 2 y = 1 z = 0 However, this is not ...