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
37 views

How to solve simultaneous inequalities (reasked)? [duplicate]

I am doing multivariable calculus, and specifically double integrals. I am facing difficulties finding the domain of the integal, however i am given the following equations: $$1≤2x+y≤2$$ $$0≤x−2y≤1$$ ...
-2
votes
1answer
45 views

Find an energy functional for the nonlinear viscous oscillator $x' = v$, $v' =-b(v)v-k(x)x$, $t>0$ [closed]

Consider the nonlinear viscous oscillator $$\begin{cases} x' = v\\ v' =-b(v)v-k(x)x,\quad t>0, \\ \end{cases}$$ where $(x,v)$ is the position and velocity of the oscillator. Here $b : \mathbb R\...
0
votes
1answer
21 views

Showing that a system has a unique steady state at $(0, 0).$

Consider a system: $$ dx/dt = y + x(2 − x^2 − y^2 ), $$ $$dy/dt = −x + y(1 − x^2 − y^2)$$ (i) Show that the system has a unique steady state at $(0, 0).$ My immediate thought is to simply ...
0
votes
0answers
10 views

Hyperplane and cubic curves and their intersections.

Solve the following: $$a^4-a^2+A_{1}E u=0;$$ $$b^4-b^2+A_{2}Eu=0;$$ $$c^4-c^2+A_{3}Eu=0;$$ $$d^4-d^2+A_{4}Eu=0;$$ and $$a^2+b^2+c^2+d^2=E,$$ for $a, b, c, d,$ and $u$, when $A_{1}, A_{2}, A_{3}, A_{4}...
0
votes
1answer
29 views

Question regarding systems of equations

If I have the following system of equations: $2+x^2-y^2=0$ $x^2-y^2-2=0$ And if I substitute $y$ by a function of $x$ and vice versa I get: $2+x^2-x^2+2=0$ $y^2-y^2-4=0$ I therefore get: ...
0
votes
0answers
20 views

Linear algebra: Solving for the coefficients on vectors

I am solving the following system: $$ -\frac{1}{r^2}\begin{bmatrix}\sqrt{\mu}\cos(\theta)\\ \sin(\theta) \end{bmatrix}= (v_r'-v_{\theta}\theta')\begin{bmatrix}\frac{\cos(\theta)}{\sqrt{\mu}...
0
votes
2answers
47 views

Find the eigenvector and eigenvalues for the following 3 x 3 Matrix?

$$ \pmatrix{5 & 8 & 16 \\ 4 & 1 & 8 \\ -4 &-4 & -11} $$ I already got the eigenvalues that is $\lambda = 1$ and $-3$. And I managed to solve the eigenvector corresponding to ...
3
votes
5answers
65 views

Solution of $x^y=y^x$ and $x^2=y^3$

Solve the given set of equations: $x^y=y^x$ and $x^2=y^3$ where $x,y \in \mathbb{R}$ Would any other solution exist other that $x=y=1$ because I think $x^2=y^3$ will only be true for $x=y=1$ or $x=y=...
0
votes
1answer
22 views

Point of intersection of ellipses

If two ellipses are intersecting at a point,is it necessary that the line drawn joining the centre of those two ellipses should also pass through the point of intersection (of ellipse)? (if yes,how to ...
0
votes
0answers
20 views

Solving systems of linear equations with complex numbers by hand

How can I solve a 3x3 system of linear equations with complex numbers by hand without making a mistake? I know that I can solve them either with Gaussian Elimination or Cramer's rule, but I find it ...
1
vote
1answer
48 views

How to estimate the parameters of a logistic differential equation from the values of its solution at times 0, 1 and 2?

How do I solve this system of equations? I received these equations after letting Wolfram Alpha solve the logistic differential equation $$N'(t)=kN(t)(M-N(t)),\qquad N(0)=65,$$ that outputs: $$N(t)=\...
0
votes
1answer
43 views

Solve $Ax=b$ for $A$ in MATLAB

I have this linear system $$\begin{bmatrix} cY(t-1)\\ acY(t-1) - acY(t-2)\end{bmatrix} = T \begin{bmatrix} Y(t-2)\\ Y(t-1)\end{bmatrix}$$ where both $c$ and $a$ are known constants, and I need to ...
0
votes
2answers
82 views

Solve the simultaneous equations for real numbers $x$ and $y$: $ \sqrt{x+a} + \sqrt{x-a} = 3 $ and $ x+y=5 $

Question: Let $a$ be a real number. Solve the simultaneous equations for real numbers $x$ and $y$: $$ \sqrt{x+a} + \sqrt{x-a} = 3 $$ $$ x+y=5 $$ My attempt: Consider the ...
2
votes
0answers
40 views

Solving a 1D integral with system of equations for retarded electromagnetic fields

I need to solve the following integral to calculate the effect of retarded electromagnetic fields on a test charge: $\int\limits_0^\zeta\frac{(\psi-(1+x)\sin(\psi+\alpha))(\frac{\psi^2}{2\beta^2(1+x)}...
1
vote
2answers
43 views

Solving a system of equations which contain sin and cosine terms.

Hello my question is the following: Solve the given system of equations: $$E=\frac{l_{p}}{\pi}\sqrt{\sin^{2}\left(\frac{\pi y_{1}}{l_{p}}\right)+\sin^{2}\left(\frac{\pi y_{2}}{l_{p}}\right)+\sin^{2}\...
0
votes
1answer
74 views

When I know $a+b+c, a^2+a^2+b^2, a^3+b^3+c^3$, then how can I find the $a$ and $b$ and $ c$ [closed]

When I know $$a+b+c = A$$ $$a^2+a^2+b^2 = B $$ $$a^3+b^3+c^3 = C$$ Then how can I find the $a$ and $b$ and $c$?
0
votes
1answer
30 views

Solutions to set of equations involving prime numbers

Is there a collection of distinct positive integers $(k_1, k_2, k_3, p_1, p_2, p_3)$ such that: $p_1, p_2, p_3$ are odd primes, and $k_1, k_2, k_3$ are odd $(k_1 + 2) p_1 = k_2 p_2$ and $(k_2 + 2) ...
1
vote
0answers
23 views

Transform the system of trigonometric equations

How to extract $\ell$ and $L$ from the following system of equations: $$\alpha=\arctan {R_E \cos \ell \sin L \over R_0 + R_E(1 - \cos \ell \cos L) }$$ $$\beta=\arctan {R_E \sin \ell \cos \alpha \over ...
4
votes
2answers
85 views

How to solve simultaneous inequalities?

I am doing multivariable calculus, and specifically double integrals. I am facing difficulties finding the domain of the integal, however i am given the following equations: $$1 ≤ 2x+y ≤ 2$$ $$0 ≤ x-...
1
vote
1answer
55 views

solve pairs of two variable simultaneous linear modular equations

I’m looking for a method to solve pairs of simultaneous linear modular equations, such as 323x + 37y = 0 Mod 243; -397x + 683y = 0 Mod 32 I’ve simplified this to 80x+37y = 243g; 19x+11y = ...
1
vote
0answers
33 views

Does anyone have nice explanation about the theory? [closed]

I have hard time interpreting the Floquet theory. Does anyone have nice explanation about the theory?
0
votes
1answer
15 views

Arbitrary variable in matrix, when there are 0 solutions, 1 solution, infinitely many solutions

For what value of the constants k does the system have (i) no solutions, (ii) infinitely many solutions, (iii) a unique solution? $$ x − 2y + z = 7\\ x − 2y − kz = k\\ kx − 2y + kz = 7 $$ At ...
-2
votes
2answers
31 views

Figuring $x$ and $y$ from two linear equations

I have a mini exam in a month to study for and I'm looking at systems of equations at the moment. I have this question to look at right now: Find $x$ and $y:$ $x-5y+4=1$ $\dfrac{x+1}{2}=y^2$ Now ...
4
votes
0answers
101 views

Large system of nonlinear equations

I am trying to solve a problem, which I find quite hard, like, headache-hard. I have to solve the following set of $M$ nonlinear equations: $$F(X)=\begin{bmatrix}f_1 (X)\\f_2 (X)\\...\\f_M (X)\\ \end{...
4
votes
1answer
49 views

Solution to a simple system of quadratic equations

I am hoping to find a closed-form solution to the following system of $n$ quadratic equations: $$ x_j^2 = \sum_{i=1}^n B_{ij}x_i $$ for $j\in\{1,\dots,n\}$, where $B_{ij}\geq 0$. There is a trivial ...
0
votes
0answers
30 views

How to determine this system of ODE's?

I'm facing this problem: "Suppose you have this system of ODE's: $\begin{pmatrix} \dot y (t)\\ \dot x (t) \end{pmatrix} = \begin{pmatrix} a & b\\ c & d \end{pmatrix} \begin{pmatrix} y (t)\\ ...
1
vote
3answers
22 views

Express last equation of system as sum of multiples of first two equations

The question says to 'Express the last equation of each system as a sum of multiples of the first two equations." System in question being: $ x_1+x_2+x_3=1 $ $ 2x_1-x_2+3x_3=3 $ $ x_1-2x_2+2x_3=...
1
vote
2answers
53 views

For which $\lambda$ do we have solutions

I'm trying to find for what values of $\lambda$ the following matrix has either no solutions, infinitely many or unique solutions. $$A=\begin{pmatrix} 1 & 1 & \lambda & 1 \\ 4 & \...
0
votes
1answer
52 views

How do you solve a system of equations with e^x

How do you solve a system of equations with e^x. For example
0
votes
0answers
17 views

Hardness of Solving multivariate quadratic systems

I know that solve multivariate quadratic systems over finite finite fields is a problem NP-Complete, but for instances that can be solved by computers, (e.g. using the F4 algorithm), my doubt is, ...
0
votes
2answers
159 views

Can some inequalities help to pin down an unique solution in a linear system of equations with infinite solutions?

I need to discuss the number of solutions of the following system of equations. Any help would be very appreciated. Consider the known parameters $a_1,...,a_4;d_1,d_2,d_3$ such that $0< a_i< ...
3
votes
0answers
108 views

Solving equation involving factorials

I have this particular equation $\frac{(\alpha-1)!(\beta-1)!}{(\alpha+\beta-1)!} = \frac{\Gamma(p)(1+q)^{n+2p} 2^n}{q^{p}(2+q)^{n+p}}$. Now, given the values of $\alpha$ and $\beta$, I need to find ...
1
vote
0answers
6 views

Closed-form solution for a simple system of concave equations

I am trying to solve what looks like a simple system of equations: $$x_j = A_j\left(\sum_{i=1}^n B_{ij} x_i\right)^\alpha $$ for all $j\in\{1,\dots,n\}$, where $n$ is a positive integer, $0<\...
1
vote
1answer
30 views

How many Cantaloupes and Watermelons should I sell?

So I want to sell cantaloupes and watermelons at a farmers market from July - Sept. and I want to make at least $450$. If I want to sell the cantaloupes for $5.50$ each and the watermelons for $6.75$ ...
-2
votes
3answers
49 views

Solve the system $ \begin{cases} x+y=m\quad \text{where } x=m-y\\ (x-a)^2+y^2=m^2 \end{cases} $

I'm trying to resolve a system of equations, but I can't solve it for $y$. Solve this for $y$: $$ \begin{cases} x+y=m\quad \text{where } x=m-y\\ (x-a)^2+y^2=m^2 \end{cases} $$ Could someone ...
0
votes
1answer
33 views

How do I prove that this system has a unique solution?

Let $V=(\mathbb R^N,(\cdot,\cdot))$, where $(\cdot,\cdot)$ denotes the standard Euclidean inner product. Let $A$ be a $N \times N$ positive definite matrix. Let $B$ be a $M \times N$ matrix, with $M \...
0
votes
2answers
38 views

An equation with a parameter

Given the equation $(|x+1|+|x-a|)^2-2(|x+1|+|x-a|)+4a-4a^2=0$ find all possible $a$ such that this equation has only one solution. I wanted to solve it like this: $(|x+1|+|x-a|)^2-2(|x+1|+|x-a|)+4a-...
1
vote
1answer
17 views

Simultaneous equations change expression variables

I have a deceptively simple-looking problem. $$A + B = A'\\ C + D = B'\\ A + C = C'\\ B + D = D'$$ On LHS $4$ variables $A, B, C, D$ On RHS $4$ variables $A', B', C', D'$ Is it possible to ...
1
vote
3answers
87 views

How to solve this equation algebraically [closed]

Solve the following simultaneous equations on the set of real numbers: \begin{cases}x^2 + y^3 = x+1 \\ x^3+y^2=y+1\end{cases} Thanks for helping!
1
vote
0answers
16 views

Terminology for asserting truth of equality/inequality based on symbolic equalities/inequalities

This may seem silly, but I am curious about algorithms used to computationally assert the truthiness (true, false, or unknown) of symbolic statements subject to a set of inequality constraints, for ...
0
votes
2answers
56 views

Solving for an unknown symmetric matrix using an answer found by a commutator.

Suppose I have, for $A,X$ real square symmetric matrices, and $B$ skew-symmetric and real, $AX-XA=B$, with $B$ and $A$ known and $X$ unknown. What properties of $X$ need to be satisfied to find $X$ ...
2
votes
0answers
20 views

Homotopy continuations for solving systems of equations over a finite field

A way of solving systems of polynomial equations over $\mathbb{R}$ or $\mathbb{C}$ is using homotopy continuation. Roughly speaking this method uses a homotopy that starts from some system of ...
2
votes
3answers
75 views

Solve the system of equations $x+2^x=y+2^y$ and $x^2+xy+y^2=12$

$$x+2^x=y+2^y$$ $$x^2+xy+y^2=12$$ I'm having trouble solving this problem, please do not solve the entire problem, I just want a hint. I don't have any good idea.
0
votes
1answer
40 views

Are there any tricks for simultaneous equations I should be aware of?

I'm at the end of a difficult logarithms question and have ascertained the linear equations I need in order to establish x and y as the questions asks of me. The equations are: $x - 5y + 4 = 1$ $\...
1
vote
1answer
20 views

Help or hint with solving system of polynomial equations.

After few years my math skills got a bit rusty and I don't seem to remember how to classify and solve a problem I'm lookin at. I have four equations and four variables: $a_xt^2 +At + B=0$ $a_yt^2 +...
4
votes
1answer
145 views

Explicit solution to a Rayleigh quotient equation

For 5 months! I have been struggling to solve the following equations analytically without numeric method (i,e, Newton method): Main equation: $$ \biggl(M^2-\cfrac{\mathbf{x^{\text{T}}}M^2\...
0
votes
1answer
60 views

Ratio & simultaneous linear equation

A pharmacist needs to combine a $2\%$ solution of a medication with a $25\%$ solution (of the SAME medication) to make $9$ litres of a $3\%$ solution. Use simultaneous linear equations to determine ...
0
votes
6answers
40 views

How to find the area of a triangle with two equations?

So I was given the following problem : ABC is a right angled triangle with the sides $a,b,c$ . Find the area of this triangle, given that $$a+b+c = 22$$ $$a^2+b^2+c^2 = 200$$ I've tried to do a lot ...
1
vote
1answer
22 views

Is there a general formula for the $n$'th variable of the solution for a lower triangular linear system of equations?

I have a countably infinite linear system of equations $Ax = b$, where $A$ is lower triangular with $-1$ at all diagonal entries, and $b = \{-1/2,0,0,...,0\}^T$. I.e the $n$'th unknown depends solely ...
2
votes
2answers
158 views

Solving Three equations for 3 Unknowns

Today I have a question and I am really curious to know about this. Question: $$ 16y+39z+50zy=0$$ $$ 85x-78z+95zx=0$$ $$ 85x+32y+70xy=0$$ $$\text{Are The Equations like these can be solve for ...