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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1
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3answers
180 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
-1
votes
2answers
44 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
50 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: $x=?, y=-1/7$
-3
votes
1answer
47 views

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

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
0answers
145 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
58 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
vote
3answers
261 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
43 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 ...
0
votes
1answer
22 views

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

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
511 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\\ ...
3
votes
0answers
43 views
+50

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
24 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
41 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
58 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
11 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 $N \in \mathbb{N}$, $m_k \in \mathbb{C}$, ...
4
votes
3answers
591 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
33 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
28 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 ...
-8
votes
1answer
43 views

Simultaneous equations, 4 unknowns [closed]

I need this solved as soon as possible $$\begin{cases} -3=x+2y+4z+8a \\ 2=x+4y+16z+64a \\ 3=x+5y+25z+125a \\ 5=x+6y+36z+216a \\ \end{cases}$$
-1
votes
1answer
44 views

Find all possible values of $\phi$: $2(2^{\phi}-1)\phi^2 + (2^{\phi^2}-2)\phi = 2^{\phi+1}-2$ [closed]

Find all possible values of $\phi$ in the following expression: $$2(2^{\phi}-1)\phi^2 + (2^{\phi^2}-2)\phi = 2^{\phi+1}-2$$
-3
votes
2answers
30 views

want to know about probability? [closed]

A certain fruit stand sold apples for \$0.70 each and bananas for \$0.50 each. if a customer purchased both apples and bananas from the stand for a total of \$6.30, what total number of apples and ...
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
52 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
32 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
5answers
49 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
17 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
161 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
21 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
37 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
80 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
23 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
1answer
37 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
28 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: ...
4
votes
0answers
36 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
44 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
30 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
23 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 ...
2
votes
5answers
112 views

I need Integer Solution to this Equation

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 ...
3
votes
2answers
227 views

How exactly do we do Gauss elimination?

This is a matrix: $$\begin{bmatrix} 1 & 1 & 1\\ 1 & 2 & 3\\ 1 & 3 & k \end{bmatrix}\begin{bmatrix} x\\ y\\ z \end{bmatrix}= \begin{bmatrix} 3\\ 6\\ 4+k \end{bmatrix}$$ ...
0
votes
2answers
24 views

Resolve this system:

Im tried to resolve this problem: $$\max\quad f\left( x,y \right) =xy\quad \text{s.a}\quad \begin{cases} x^2 +y^2+z^2 -1=0 \\ x+y+z=0 \end{cases}$$ Well, i form the lagrangian and the respective ...
1
vote
0answers
16 views

Is there a way to delineate the parameter of highest influence in a system of differential equations?

So I have a system of nonlinear ordinary differential equations dependent on parameters. These equations can traditionally be solved numerically with robust methods and the solution is well defined. ...
-1
votes
3answers
23 views

Solve problems using linear system. [closed]

One metal alloy is $25\%$ copper, another is $50\%$. How much of each should be used to make $500$g of an alloy that is $45\%$ copper?
3
votes
4answers
92 views

Quick way to solve the system $\displaystyle \left( \frac{3}{2} \right)^{x-y} - \left( \frac{2}{3} \right)^{x-y} = \frac{65}{36}$, $xy-x+y=118$.

Consider the system $$\begin{aligned} \left( \frac{3}{2} \right)^{x-y} - \left( \frac{2}{3} \right)^{x-y} & = \frac{65}{36}, \\ xy -x +y & = 118. \end{aligned}$$ I have solved it by ...
3
votes
1answer
37 views

Fruit vendor selling fruit

This is a very interesting word problem that I came across in an old textbook of mine. So I know its got something to do with simultaneous diophantine equations, but other than that, the textbook gave ...
1
vote
3answers
69 views

Solving a three variable equation

I have three given values, suppose a=1.86, b=2.6 and c=4.2. Now I have to figure out x,y,z such that $x\gt 0,y\gt 0$ and $z\gt 0$ $x+y+z=1$ $a*x\gt 1, b*y\gt 1$ and $cz\gt 1$ I need a ...
1
vote
1answer
76 views

solve system equation: $ 2a^2 - 1 = b, 2b^2 - 1 = c, 2c^2 - 1 = a $

I have this system equation: $$ 2a^2 - 1 = b $$ $$ 2b^2 - 1 = c $$ $$ 2c^2 - 1 = a $$ From system equation we see that $ a \neq 0 , b \neq 0, c \neq 0 $ , so : $ 2a^2 - 1 \neq 0 => a \neq ...
0
votes
1answer
33 views

Proving that if $ad-bc \neq 0$ then there is an unique solution to the linear system with 2 unknowns and 2 equations

Exercise: Prove that if $ad-bc \neq 0$, then the system $$ ax + by = j \\ cx + dy = k $$ has an unique solution. This is from the very first subsection of Hefferon's Linear Algebra, and also the ...