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.

learn more… | top users | synonyms (1)

-3
votes
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!
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
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 ...
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
24 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
1answer
38 views

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
21 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
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. ...
3
votes
1answer
63 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
56 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
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
votes
3answers
55 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
545 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
7 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
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: $$\frac{d^2 M_N}{d x^2}=\lambda_{N}^2 M_N$$ $$\frac{d^2 M_{N-1}}{d x^2}=\lambda_{N-1}^2 M_{N-1}-\frac{f}{d_{N-1}}M_N$$ ...
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
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. ...
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 ...
-2
votes
1answer
70 views

Algorithm Maths Question [closed]

Hi I'm stuck on this maths question don't really know how to about it. I've tried simultaneous equation to solve for a and b with no success. Hope you can help. A program looks up a specific entry ...
7
votes
4answers
458 views

Exponential Simultaneous Equations

Solve the following simultaneous equations: $$2^x + 2^y = 10$$ $$x + y = 4$$ Looking at it, it is obvious that the answers are $(3,1)$ and $(1,3)$, however, I was wondering if they could be solved ...
0
votes
0answers
10 views

How do I choose the appropriate eigenvalues for Kinetic Component Analysis (or an Extended Kalman Filter)?

KCA (Kinetic Component Analysis) basically applies an Extended Kalman Filter after a taylor series expansion of a signal. By using this state space approach, the noise is reduced, and predictions can ...
0
votes
1answer
43 views

Splitting a 2nd order PDE into a system of first order PDEs/ODEs

Consider a standard wave equation: $ \frac{\partial^2 p}{\partial t^2} = c^2 \frac{\partial^2 p}{\partial x^2} $ The question is how to formulate this as a first order system: $ \frac{\partial ...
0
votes
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
votes
1answer
46 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
votes
1answer
25 views

Solving inhomogenous continuous-time system with non-diagonalisable system matrix

I have an exercise where i have to find the general solution to this problem: $$ X'=\left( \begin{matrix} 2&-1\\ 4&-2 \end{matrix} \right)X + \begin{pmatrix} 2\\1 \end {pmatrix}. $$ ...