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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0
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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
460 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
45 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
51 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: $$ X'=\left( \begin{matrix} 2&-1\\ 4&-2 \end{matrix} \right)X + \begin{pmatrix} 2\\1 \end {pmatrix}. $$ ...
1
vote
0answers
35 views

Solving Linear equations using Conjugate gradient method

Given this two linear equations $$\begin{cases} 3x-y=1 \\ -{ x }+2y=-1 \end{cases}\\ $$ How can this system be solved iteratively with the Conjugate Gradient method?
2
votes
1answer
38 views

Non linear system of differential equations

Is there a specific name to the following type of non linear ODEs $\begin{array}{c} \dot{x}_1 &= c_1 \, x_2\, x_3 \\ \dot{x}_2 &= \, c_2 x_1 x_3 \\ \dot{x}_3 &= c_3 \, x_2 x_1 ...
0
votes
1answer
30 views

How do you go about solving partial differential equations for finding critical points in general optimization problems?

I was reading about partial second derivative test for optimization problems and I came across the example here. I saw the equations have yielded four critical points, but I wasn't able to find those ...
2
votes
2answers
123 views

System of equations on $\mathbb{Z}$

Knowing that $a,b,c,d,e,f \in \mathbb{Z}$ solve the system: $$ \begin{align} 18&=cf \\ 27&=ce+bf \\ 28&=af+be+cd \\ 22&=f+ae+bd+c \\ 11&=e+b+ad \\ 5&=a+d \end{align} $$ I want ...
2
votes
0answers
22 views

Locating a point in 2D using only differences between distances

Let $R_1,R_2,R_3,R_4,T$ be points on a 2D plane, as in this figure. $R_1,R_2,R_3,R_4$ are reference points with known positions. The goal is to find the position of $T$. $d$ is the Euclidean ...
0
votes
1answer
34 views

Finding a generating set of vectors

I want to solve the following task: Find the minimal generating set (german: "minimales Erzeugendensystem") for the set S: S = { $\begin{pmatrix} 1 \\ 1 \\ 0 \\1\\1 \end{pmatrix}$, ...
3
votes
1answer
44 views

Injectivity of transformation

Is transformation $g:x=(x_1,x_2,x_3)\mapsto \frac{x}{\|x\|}$ injective? What if $x_1=1$?
3
votes
1answer
48 views

Solving nonlinear system

I have the following nonlinear system $$\begin{cases} y_1 = \frac{x_1}{\sqrt{x_1^2+x_2^2+x_3^2}} \\ y_2 = \frac{x_2}{\sqrt{x_1^2+x_2^2+x_3^2}} \\ y_3 = \frac{x_3}{\sqrt{x_1^2+x_2^2+x_3^2}} \end{cases} ...
0
votes
1answer
23 views

Help on Solutions to Systems of Equations

Here is a screenshot: http://imgur.com/gallery/Wh6ksgO/new I was looking at my Linear Algebra quiz solutions and I saw the following: "Thus from RREF, we can see the system if consistent and contains ...
0
votes
0answers
28 views

Learning to solve complex inequalities in many variables

below is a very specific inequality problem. I would like to know how to solve it so I can apply it to more complex problems. The equations are as follows: $$3.5x−2.5y−3z=A$$ $$−7.5x+3.75y+5.25z=B$$ ...
0
votes
3answers
52 views

Finding the kernel of a linear map

Our exercise is to find all solutions to the equation $Ax = 0$, among others for the following matrix $$A =\begin{pmatrix} 6 & 3 & -9 \\ 2 & 1 & -3 \\ -4 & -2 & 6 ...
0
votes
0answers
23 views

Binary solutions of multivariate polynomial system in special (factored) form.

In my personal research I've run into a system of multivariate polynomials (with coefficients in a field). I am aware that there is no polynomial time algorithm (in the number of indeterminates) for ...
0
votes
3answers
63 views

Solving this Cubic equation

$(x^2+y)(x+y^2)=(x+y)^3$ Can $x^2+y^2$ attain values $2$ and $13$? How to approach this question I tried solving this equation and couldn't solve after this: $$xy+1=3(x+y) $$
1
vote
1answer
82 views

Finding $a^{2014} + b^{2014} + c^{2014}$ given some conditions on $a,b,c$.

I came across this problem: "Let $a$, $b$, $c$ be nonzero real numbers that satisfy the conditions : $$a + b + c = 9,\\\mathrm{and}~ab + bc + ca = 27 $$ Calculate $$a^{2014} + b^{2014} + ...
0
votes
3answers
47 views

Add or subtract something to a number to reduce it to the range 0 to 24

I'm developing a C++ program and I need to find a formula that given a number to reduce and a limit number, get a value between 0 and this limit number. I don't know if it is allow to put C++ code ...
0
votes
2answers
69 views

Find all the possible real values for $a,b,c,d$.

Let pairs $(a,c)$ and $(b,d)$ be roots of the equations $x^2 + ax - b = 0$ and $x^2 + cx + d = 0$ respectively. Find all possible real values for $a,b,c,d$.
0
votes
1answer
41 views

Find function by 2 tangents and 2 points

I am looking for explicit function descriptions $F_1(s)$ and $F_2(s)$, following the line plotted. The line is just a description, but $F_1$ should never exceed $F_m$ and start at $s_0$ with a tangent ...
1
vote
2answers
64 views

How to solve this equation numerically???

The equation is given by $$ \sum_{n=1}^N \min(\gamma, \beta a_n)=N$$ where $\beta$ is the variable with $\beta\in[0,\sqrt\gamma/\min(a_n\mid a_n>0)]$, $ \gamma $ is a constant with ...
-1
votes
2answers
24 views

System of equation problem [closed]

Let $A$ be a $3 \times 3$ matrix made from the variable coefficient of the following system. Let $B$ be a $3 \times 1$ matrix made from the coefficients of the right hand side. Solve the system by ...
2
votes
1answer
63 views

Is there a numerical solution for a system of three 1st order nonlinear ODE?

How would I go about solving the following system of non-linear ODEs for $x(t), y(t), z(t)$ $$x' = y $$ $$y'=\sin(x)+z$$ $$z'=y-z$$ I have the following initial conditions; $$x(0) = 0$$ ...
2
votes
3answers
86 views

Solve the equation $4\sqrt{2-x^2}=-x^3-x^2+3x+3$

Solve the equation in $\Bbb R$: $$4\sqrt{2-x^2}=-x^3-x^2+3x+3$$ Is there a unique solution $x=1$? I have trouble when I try to prove it. I really appreciate if some one can help me. Thanks!
3
votes
1answer
23 views

Solving Equations system question

We get this equation and need to solve Solve in $\mathbb{Z} $ the given equation $ y(y -x )(x+1) = 12\ $
1
vote
1answer
55 views

Trouble Solving a system of 3 equations

I'm having trouble solving a system of 3 equations. The set of equations in question is shown below $C_a=\frac{R_a}{\frac{R_a}{r_a}+\frac{R_b}{r_b}+\frac{R_c}{r_c}}, \quad ...
1
vote
2answers
52 views

Solving two diophantine equations.

Find at least one 5-tuple of positive integers which satisfy the following two equations $$a^2-d^2=3(b^2-c^2)$$ $$e^2-b^2=3(d^2-c^2)$$ such that no three of the 5 positive integers $a, b, c, d, e$ ...
0
votes
2answers
42 views

How do I solve a linear system with two variables and three equations?

To be specific here is the system: $$x-2y=0 \tag{1}$$ $$x-2(k+2)y=0 \tag{2}$$ $$x-(k+3)y=-k \tag{3}$$ I have already solved it for equations $(1)$ and $(2)$... what should I do with the 3rd ...
2
votes
1answer
15 views

Commutative Monoid - matrix set

Let $M$={$\begin{bmatrix} a & b & c \\ c & a & b \\ b & c & a \end{bmatrix}|a,b,c\in \mathbb{R}, a+b+c=0$}. The matrices in $M$ are a special kind of Toeplitz matrices ...
2
votes
4answers
168 views

Do row operations change the column space of a matrix?

I know that (i) row operations do not change the row space (ii) column operations do not change the column space and (iii) row rank = column rank (but this is sort of unrelated, I think). But, ...
0
votes
0answers
29 views

system of equations using the Elimination Method

Solve the system of equations using the Elimination Method. 3x-4y+0z=63 -2x-1y+0z=-9 5x-3y+0z=72 (x,y,z)=( , , ) I have tried this a couple of times and ...
1
vote
0answers
24 views

Systems of equations word problem

A goldsmith has two alloys, the first containing $77\%$ and the second containing $96\%$. If $x$ grams of the first alloy are mixed with $y$ grams of the second, obtaining $100$ grams of an alloy ...
8
votes
1answer
123 views

Evaluate $a^2+b^2+c^2$

I found this questions from past year maths competition in my country, I've tried any possible way to find it, but it is just way too hard. If $a, b, c$ are distinct numbers such that $a^2 - bc = ...
0
votes
2answers
52 views

Elementary Substitution in Solving Equations - Why it works

To solve a system of linear and certain non-linear equations, the substitution method is widely used by elementary and high school students. As explained here, to solve this simple system of linear ...
0
votes
0answers
62 views

System of equations to solve this nested radical.

The nested radical $$1.75793\approx\sqrt{1+\sqrt{2+\sqrt{3+\cdots}}}$$ has yet to be given a closed form. However, nested radicals of the form, $$\sqrt{A+B\sqrt{A+B\sqrt{A+\cdots}}}$$ have the ...
3
votes
2answers
60 views

Solve $\begin{cases} x + y + z = 2 \\ 2xy - z^2 = 4 \\ \end{cases} $ for x, y, z.

It came to my mind to rewrite the expression above as $$\begin{cases} x + y = 2 - z \\ 2xy = (2 - z)^2 + 4z \\ \end{cases} $$ and see if there any restrictions on the values of the variables occur. ...
0
votes
1answer
27 views

System of equations problem?

In a chemistry class, 3 liters of a 4% silver iodine solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? Equation: .10x + .04(3-x) = ...
1
vote
5answers
174 views

Find $x$ if $\frac {1} {x} + \frac {1} {y+z} = \frac {1} {2}$ [closed]

I found this question from past year's maths competition in my country. I've tried any possible way to find it, but it is just way too hard. Find $x$ if \begin{align}\frac {1} {x} + \frac {1} ...
2
votes
2answers
103 views

Systems of equation with only 1 equations?

So this is a system of equations problem only there's 1 equation as far as I could tell? Roberto invested some money at 7% and then invested 2000 more than twice this amount at 10% His total anual ...
0
votes
0answers
27 views

Existence and uniqueness of a pde solution

I have the PDE system: $\frac{\delta}{\delta t}u(t,r)=-\int_0^1 H(|r-r'|)v(t,r')dr'u(t,r)$ $\frac{\delta}{\delta t}v(t,r)=\int_0^1 H(|r-r'|)v(t,r')dr'u(t,r)-v(t,r)$ $x(0,r)=\rho(r), ...
2
votes
2answers
36 views

Coupled second-order differential equations

I am trying to solve the following system of coupled ODEs: \begin{align} -x^2 f'' - 3xf' + (1-2a)f - (a+1)x^2g'' + (2-4a)xg' + (4a-2)g &= 0,\\ (a-1)x^2 f'' + (4a+2)xf' + (12-6a)f + 12xg' + ...
3
votes
1answer
37 views

Cramer Rule Over Finite Field

Let $A=\pmatrix{4&2\\ 0&1},\ b=\pmatrix{5\\ 3}$ and $A\pmatrix{x_1\\ x_2}=b$ over the field $\mathbb Z_7$. What is $x_1$? So we need to calculate $$x_1=\frac{\det(A_1)}{\det(A)}$$ ...