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)

1
vote
1answer
52 views

Mapping the intersection of hyperplanes/simplex to lower-dimensional unit-simplex

Suppose I have an object in $\mathbb{R}^5$ described by: $$x_1+x_2+x_3+x_4+x_5=1$$ $$x_1+2x_2+3x_3+4x_4+5x_5=6$$ $$x_1+7x_2+8x_3+9x_4+10x_5=11$$ $$x_1,x_2,x_3,x_4,x_5 \geq 0$$ Is there a way that I ...
1
vote
1answer
21 views

Given two variables and their ranges, get a third value.

I'm building a model but I got stuck at this: I have $x,y$ whose ranges are ($10,000$ to $2,000,000$) and (1 to 36) respectively. Also I have a z that ranges from 16 to 30. I know their relations in ...
1
vote
1answer
29 views

Find the end points of a line segment in 3D space

I have a line segment in 3 dimensional space (x,y,z), and I want to find the 2 endpoints of this line segment. Is there a systematic way of doing this? To be specific, I have the line described by ...
-2
votes
2answers
61 views

how to solve nonlinear system of equations

I have $A, B, C, D, E, F.$ I want to calculate a and b from the following system of equations: I know I should solve this system using $3$ equations and $3$ unknowns, but it is not linear. can any ...
0
votes
0answers
19 views

How is equivalency of linear systems defined?

Still kind of new to the world of proofs in math so I ask: Is it that linear systems are equivalent if they have the same solution set or Is it that linear systems are equivalent if and only if ...
2
votes
1answer
30 views

System of Congruences with Special Symmetry

Show that the following system of congruences \begin{align} \begin{cases} 3 x^4 - 7 x^2 y^2 - 7 x^2 z^2 - 35 y^2 z^2 \equiv 0 \pmod{p} \\ 3 y^4 - 7 x^2 y^2 - 7 y^2 z^2 - 35 x^2 z^2 \equiv 0 \pmod{p} ...
3
votes
0answers
37 views

Solving simultaneous equations in complex numbers

Given $z_1,z_2$ are complex numbers such that sum of their squares is a real number and $$z_1(z_1^2-3z_2^2)=2$$ and $$z_2(3z_1^2-z_2^2)=11.$$ I need to find the value of sum of squares of two complex ...
0
votes
1answer
9 views

Is there a general relationship between number of variables and of constraints?

This comes up most notably in linear algebra and differential equations - usually unique solutions come about when the number of constraints matches the number of variables, or in the case of ...
0
votes
0answers
36 views

How to solve complicated systems of equations with exponentials?

I'm trying to solve the system of equations at the bottom of this image, I need to solve for Rohm, Rdf, Rct, Cdl, Cdf, and Voc in terms of the theta parameters so I can calculate them from the ...
0
votes
2answers
32 views

Determining the coordinates of a vector with respect to a basis

Problem: Let $V = \mathbb{R}[X]_{\leq 4}$ be the vectorspace of all polynomials of degree at most $n$, and let $\alpha = \left\{1, 1 +x, (1+x)^2, (1+x)^3, (1+x)^4\right\}$ be a basis for $V$. Find the ...
3
votes
1answer
47 views

Intuitive Explanation For Why Dependent Equations Contain No Added Information?

I've always been taught that because dependent equations contain no added information they can be deleted without effecting the solution set. Now this makes sense to me if an equation is a constant ...
3
votes
1answer
60 views

transform integral to differential equations

I found a similar system of integral equations in a paper. It says that it can be solved by differentiating and then using standard techniques. My question is, how can I differentiate such a system in ...
1
vote
3answers
216 views

Find the value of $x$ such that $\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-x}}}}=x$

Find the value of $x$, $$\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-x}}}}=x$$ Help guys please, I have tried and I got, $x=-2, x=1$, and I think it's wrong
-2
votes
2answers
54 views

For what values of $a$, $b$, and $c$ the above system has: One solution. Infinitely many solutions. No solutions.

I am stuck with this now, I tried reducing the matrix to row echelon form, but it gets a bit hard. Is there not a simpler way? The system is: \begin{align*} a x + b y − 3 z &= −3\\ −2 x − b y + ...
1
vote
3answers
56 views

Simultaneous equation with fractional solutions.

How do you get to find $x$ when $y$ is a fraction ? Anyone mind to explain it step by step for the clearest explanation.=) $$-7x +2y = 2$$ $$14x + 3y = -5$$ Answer: $x=?, y=-1/7$
-4
votes
1answer
51 views

solve $(x-3)^2 + (x+1)^2 + (4x-5)^2=0$ [closed]

solve $(x-3)^2 + (x+1)^2 + (4x-5)^2=0$ this is what I have tried $$(x-3)^2=(x+1)^2=(4x-5)^2=0$$ $$x=3, x=-1, x=\frac{5}{4}$$
1
vote
1answer
330 views

Apollonian gasket

Okay , is there a way to find the radius of the nth circle in a apollonian gasket .. Something like this Its like simple case of apollonian gasket .. I found from descartes' theorem $R_n = ...
0
votes
0answers
84 views

A good equation system

Given $a,b,c$ positive numbers, solve the system $\sqrt{xy}+\sqrt{xz}-x=a$, $\sqrt{yz}+\sqrt{yx}-y=b$ and $\sqrt{zx}+\sqrt{zy}-z=c$, where $x,y,z\in \mathbb{R}$. This only a pretty question. I did ...
-1
votes
3answers
280 views

If 6x = y+z and 4x = y-z, express z in terms of x

\begin{align} 6x &= y+z\\ 4x &= y-z \end{align} How to express $z$ in terms of $x$? I'm not 100% sure on how to solve in terms of x
1
vote
4answers
46 views

How to find a real matrix with complex eigenvalues,

Give a $2 \times 2$ real matrix $A$ with eigenvalues $2+3i$, $2-3i$. I would like hints only. So far, I've been trying get somewhere with $\det[A-(2+3i)I] = 0$ and $\det[A-(2-3i)I] = 0$; which ...
-1
votes
1answer
28 views

How do i show stability of fixed points of this two.dimensioanl system:$f(x,y)=(y,y²−x²)$? [on hold]

Is there someone show me how do i show stability of fixed points of this two.dimensioanl system:$$f(x,y)=(y,y²−x²)$$ and what is it relation to henon map ? Note :thank you for any help
11
votes
4answers
540 views

Solving a system of non-linear equations

Let $$(\star)\begin{cases} \begin{vmatrix} x&y\\ z&x\\ \end{vmatrix}=1, \\ \begin{vmatrix} y&z\\ x&y\\ \end{vmatrix}=2, \\ \begin{vmatrix} z&x\\ y&z\\ ...
5
votes
1answer
162 views

Equivalence of system of nonlinear equations

Let $A\in\mathbb{R}^{n\times n}$ be a positive semidefinite matrix, $b\in\mathbb{R}^n$, $k>0$, and $g:\mathbb{R}^n\rightarrow\mathbb{R}$ be a positive function. Consider the system of nonlinear ...
0
votes
0answers
25 views

Can I solve these simultaneous questions, and if so, how?

I have a set of paired experimental observations (Fo, Bo), e.g. 1.55, 8.52 4.56, 36.36 21.03, 64.98 (> 6 data pairs in total) which I believe can be modelled as being generated by Fo = Ft + a.Bt ...
0
votes
0answers
42 views

Solving a specific equation involving cos and sin

Here is the equation: $a\sin(\alpha+2\theta)+b\sin(\beta+\theta)=0$, where $\theta$ is the variable, $a$ and $b$ are positive, $\alpha$ and $\beta$ are constant. Please help and thank you very ...
5
votes
2answers
59 views

System of equations in a,b,c,d

$a,b,c,d$ are complex numbers satisfying \begin{cases} a+b+c+d=3 \\ a^2+ b^2+ c^2+ d^2=5 \\ a^3+ b^3+ c^3+ d^3=3 \\ a^4+ b^4+ c^4+ d^4=9 \end{cases} Find the value of the following: ...
0
votes
0answers
15 views

Another trigonometric moment problem

Is there a standard approach for solving the following system: $$ m_k = \sum_{j=1}^N a_j e^{-2\pi i \mu_j k \delta}, \quad k = 0, 1, 2, \ldots, $$ where $N \in \mathbb{N}$, $m_k \in \mathbb{C}$, ...
5
votes
4answers
621 views

Why are the coefficients always equal?

Take the equation $ax^{2} + bx + c = 3x^{2} + 4x + 53$. Why is it always true that $a = 3, b = 4$ and $c = 53$? I've seen many examples like this where the coefficients are equated, and was just ...
1
vote
1answer
36 views

Underdetermined vs Overdetermined Problem

I'm trying to create a model which is of the form $$y = (a_0 + a_1l)[b_0+\sum_{m=1}^M b_m\cos(mx-\alpha_m)] [c_0 +\sum_{n=1}^N c_n\cos(nz-\beta_n)]$$ In the above system, $l$,$x$ and $z$ are ...
1
vote
2answers
29 views

Grasping “Substitution” in terms of linear algebra

So I have a set of equations: $$x_{1} + x_{2} = 1$$ $$x_{2} + x_{4} = 3$$ From linear algebra, we know that (say, we're in $\mathbb{R}^{4}$, i.e. we have 4 variables), the solution space to the ...
1
vote
0answers
23 views

How can I solve this specific set of equations?

Here are the equations: $$\sum_{k = 1}^n i_k + Y_n u_n = J \quad \quad (1)$$ $$i_1 + Y(u_1 - u_2) = J \quad \quad (2)$$ $$i_k - Y(u_{k - 1} -2u_{k} + u_{k + 1}) = 0, \quad \quad k = 2, ..., n - 2 ...
3
votes
2answers
56 views

How to solve this system of equations for $x^2+y^2+z^2$?

For the complex numbers $x,y,z$, the system of equations $x^2-yz=i~~~~~ y^2-zx=i~~~~~ z^2-xy=i$ It is not easy for me to get $x^2+y^2+z^2$ from the above. I don't need the values of $x,y,z$ I'm ...
1
vote
3answers
51 views

When do variables cancel out?

Sometimes if I randomly combine different equation and try to solve for a variable, one of them will cancel out. Why? For example: $\displaystyle x^2 = 4y^2$ and $\displaystyle x = 2y + 1$ And solve ...
0
votes
4answers
61 views

Help Solving a Simultaneous Equation.

Im currently doing my Kumon (A math tutoring center I guess) homework, and Im having a bit of difficulty answering a simultaneous equation, involving $x$ and $y$ variables to the second power. School ...
0
votes
1answer
21 views

Parallel and distinct

As I understand it, there are three possibilities for linear systems; no solution, unique solution, or infinitely many solutions. (i) For unique solution, there is only one intersection, a point ...
3
votes
2answers
191 views

Solving $2^x - 3^x + 6^x =0$.

Are there any known methods to solve $$2^x - 3^x + 6^x = 0,$$ where $x$ is either in closed form, perhaps in terms of special functions, or to give inequalities on the answers, where $x\in\mathbb{C}$ ...
1
vote
0answers
20 views

How to properly detect rows to be swapped in a Gaussian elimination?

I'm trying to describe an algorithm for solving solvable linear systems. The Gaussian elimination is pretty straightforward in terms of adding multiples of rows. However, consider the following ...
2
votes
1answer
22 views

Name and explanation of a Numerical Analysis method for solving systems of non-linear equations

In a non-english textbook of Numerical Analysis there is a method for solving systems of non-linear equations. But not only I can't understand how this method is used but I can't even found the name ...
1
vote
1answer
44 views

solve system equation: $ a \cdot b = 3 \cdot a-b+1, b \cdot c = 3 \cdot b - c + 1, c \cdot a = 3 \cdot c - a + 1$

I want to solve this system of equations but i'm stuck. Here is it: $$ a \cdot b = 3 \cdot a - b + 1 $$ $$ b \cdot c = 3 \cdot b - c + 1 $$ $$ c \cdot a = 3 \cdot c - a + 1 $$
1
vote
2answers
17 views

System of non-homegeneous linear equations

I need to find a relation between $a$, $b$, $c$, $d$ in order the system with the following augmented matrix has at least one non-trivial solution. I have tried both the Gaussian and Gauss-Jordan ...
0
votes
2answers
83 views

Find x, if $ \log _{15}\left(\frac{2}{9}\right)^{\:}=\log _3\left(x\right)=\log _5\left(1-x\right) $

So how can I find the value of x, if: $$ \log _{15}\left(\frac{2}{9}\right)^{\:}=\log _3\left(x\right)=\log _5\left(1-x\right) $$ I tried switching everything to base 15, but that didn't work out ...
0
votes
1answer
24 views

Solve the system of equations by variable estimation

Solve the system of equations: $\left\{\begin{array}{l}(x-1)\sqrt{x-y^2}=y(x-2y+1)\\y\sqrt{x-1}+3\sqrt{x-y^2}=2x+y-1\end{array}\right.$ I guess there is only one solution $(x;y)=(2;1)$. This is my ...
0
votes
2answers
44 views

Convergence of a particular fixed point iteration scheme

Setup I have the following non-linear system of equations: $$ \mathbf{x} P(\mathbf{x}) = 0 $$ where $\mathbf{x} \in \mathbb{R}_{>0}^n$ is a probability distribution, i.e., $\sum_i x_i = 1$, and ...
0
votes
1answer
34 views

Solve the system of equations with one symmetrical equation

Solve the system of equations: $\left\{\begin{array}{l}x^3-y^3+(3x^2+y-2)\sqrt{y+1}-(3y^2+x-2)\sqrt{x+1}=0\\x^2+y^2+xy-7x-6y+14=0\end{array}\right.$ I used wolframalpha.com and got the solution: ...
5
votes
0answers
46 views

Solve the system of equations with $x=y$

Solve the system of equations: $\left\{\begin{array}{l}\sqrt{x^2+(y-2)(x-y)}+\sqrt{xy}=2y\\\sqrt{xy+x+5}-\dfrac{6x-5}{4}=\dfrac{1}{4}\left(\sqrt{2y+1}-2\right)^2\end{array}\right.$ I used ...
0
votes
1answer
27 views

How to find the position on a circle that satisfies two constraints?

Say I'm given an point P1 at coordinates $(x_1,y_1)$, and another point $P_2$ at coordinates $(x_2,y_2)$. Then I have a point $P_0$ that needs to be at coordinates $(x,y)$ such that it is a fixed ...
2
votes
2answers
45 views

Solve the follwing system of equations for $x, y$ and $z$

$$\frac{y+z}{5}=\frac{z+x}{8}=\frac{x+y}{9}$$ and $$6(x+y+z)=11$$ My teacher told me that I would have to get $3$ different equations to get $x, y$ and $z$. I've tried many methods and I'm confused ...
0
votes
0answers
32 views

When is this iteration guaranteed to converge

I have a nonlinear $N$-component equation of the form $x_n = \sum_m f_n(x_m),$ where $f$ is some function and the goal is to find a set of $x_n$ that satisfies this equation. I have experimented ...
1
vote
0answers
25 views

Lagrange multipliers, once I use the constraint equation, do I have to worry about it again later?

I am solving $ grad [f(x,y,z)]$ = $\lambda$grad[g(x,y,z)] I have then three equations, one involving x's and lambdas, another involving y's and lambdas and a third involving z's and lambdas. I then ...
1
vote
5answers
123 views

I need Integer Solution to this Equation [duplicate]

I need to know how to solve this equation where x and y are both variables Find integer Solutions. $$ \frac{1}{x} + \frac{1}{y} = \frac{1}{2} $$ from what I know I need at least 2 equations to solve ...