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)

-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{...
3
votes
1answer
47 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
21 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
51 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
13 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
158 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
86 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
55 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
142 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
56 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
21 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
151 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 ...
0
votes
1answer
35 views

Proof by induction, system of equations

We conjecture that there is a formula of the form $\sum_{j=1}^{n}{j^2} = an^3 + bn^2 + cn + d$ for all integers n ≥ 1 (3) (a) Assuming that such a formula is true, find the value of a, b, c, d. (...
0
votes
0answers
15 views

4x5 linear equation treaded as parameter

I got a 4x5 linear equation (4 equation 5 incognitas)like this: 1 1 0 0 0 = 800 0 1-1 1 0 = 300 0 0 0 1 1 = 500 1 0 0 0 1 = 600 i tried to give solution taking ...
0
votes
1answer
23 views

Have do i get 2nd equation from 3 equation 2 variable system answer?

My teacher today solved this system of equations for us that consisted of these 3 equations, 1) p0 + p1 =1 2) a*p0 + b*p1 =p0 3) c*p0 + d*p1 =p1 , ...
0
votes
3answers
24 views

Find coefficient in linear equation system for non-trivial solution (easy question)

Find the real value of $\alpha$ so that the system admits solution different from (0, 0, 0). $\begin{cases} \alpha x + y = 0 \\ \alpha y + z = 0 \\ 8x + \alpha z = 0 \end{cases}$ a) 8 b) 2 c) 1 d) -...
0
votes
0answers
40 views

How to solve these simultaneous equations?

I'm doing questions from this page: http://tartarus.org/gareth/maths/tripos/IB/Variational_Principles.pdf and I'm doing Question 2013 1/I/6A The question asks to find the cylindrical cup of least ...
0
votes
1answer
18 views

Convert line parametrization into two equations

Consider the following parametrization on $\mathbb{R}^3$ $$g(t) = (t^2,t\cos(t),t\sin(t))$$ This is a line, and as such can be characterized by two equations. I already found the first one to be $$...
2
votes
1answer
26 views

Properties of the solution of a linear system with random equations

$x_i$ is drawn from $\mathrm{unif}(a,b)$, $y_i$ is drawn from $\mathrm{unif}(c,d)$. $x_i$ are independent from each other. $y_i$ are independent from each other. $x_i$ are independent of $y_i$. $i$ ...
0
votes
2answers
66 views

Basis for intersecting subspaces - is there a trick here?

I'm doing this problem, which gives me these subspaces of $\mathbb{R}^4$ $$U=\text{span}\left\{\;\begin{pmatrix} 3\\ 2\\4 \\ -1\end{pmatrix},\;\begin{pmatrix} 1\\ 2\\1 \\ -2\end{pmatrix},\;\begin{...
0
votes
2answers
49 views

Solution to system of non linear equations

what is the best way to solve this system of equations: $$ax^2 +by^2-2y=0$$ $$axy+byz-z=0$$ $$ay^2+bz^2-c=0$$ Solve for x,y,z where a,b,c are constants.
1
vote
0answers
84 views

System of Equations which can be solved by inequalities: $(x^3+y^3)(y^3+z^3)(z^3+x^3)=8$, $\frac{x^2}{x+y}+\frac{y^2}{y+z}+\frac{z^2}{z+x}=\frac32$.

S367. Solve in positive real numbers the system of equations: \begin{gather*} (x^3+y^3)(y^3+z^3)(z^3+x^3)=8,\\ \frac{x^2}{x+y}+\frac{y^2}{y+z}+\frac{z^2}{z+x}=\frac32. \end{gather*} Proposed by ...
0
votes
2answers
60 views

Determine $x$ if $x = 4 \mod 17$ and $x = 3 \mod 11$. [closed]

Given $x =4\mod 17$ and $x = 3\mod 11$, determine $x$. I know that $\gcd(17,11)= 1$. I was hoping to use this to determine $x$.
0
votes
1answer
26 views

If $A$ is a singular square matrix, then $Ax = b \neq \vec{0}$ has $0$ or many solutions

I was reading this pdf: https://www.math.ohiou.edu/courses/math3600/lecture10.pdf and it tells you that if $A$ is a singular square matrix, then $Ax = b \neq \vec{0}$ has $0$ or many ...
1
vote
1answer
34 views

How can I write a set of equations in summation form?

I have a system of equations as follows: \begin{align} & A_1^{11} + A_1^{12} + A_1^{13} + \cdots + A_1^{1n}=X \\[8pt] & A_1^{21} + A_1^{22} + A_1^{23} + \cdots+ A_1^{2n}=X \\[8pt] & \...
0
votes
0answers
18 views

Counting the number of roots of multivariate polynomials?

The equation of a circle is well known $$(x-x_0)^2+(y-y_0)^2 - r^2 = 0$$ It has a solution all along the circle with midpoint $(x,y) = (x_0,y_0)$. We also know that $ab = 0$ whenever any of $a$ and/or ...
0
votes
1answer
35 views

solving a pair of simultaneous equations

I have a rather messy pair of simultaneous equations, which I need to solve for x: $\left(x+2n-1\over2\right)^2+\left(\sqrt{1-\left(x^2-2\over2\right)^2}+\sqrt{1-\left(-x^2+x+2n+1\over2\right)^2}\...
1
vote
2answers
43 views

So many logs with different bases

$ \large { 6 }^{ \log _{ 5 }{ x } }\log _{ 3 }( { x }^{ 5 } ) -{ 5 }^{ \log _{ 6 }{ 6x } }\log _{ 3 }{ \frac { x }{ 3 } } ={ 6 }^{ \log _{ 5 }{ 5x } }-{ 5 }^{ \log _{ 6 }{ x } }$ The sum of the ...
1
vote
2answers
43 views

Number of integral solutions for an equation

How do we approach this kind of problem of finding number of positive integral solutions to $$\frac{1}{x}+\frac{1}{y} = \frac{1}{n!}$$ Here $n$ is given.
0
votes
1answer
10 views

How is Dulac's Multiplier selected?

I'm aware that Dulac's (Negative) Criterion states that a system of differential equations of the form $x' = f(x,y), \; y' = g(x,y)$ has no periodic orbits in the plane if we can find some function $\...
0
votes
0answers
21 views

Finding the General Solution for a System of Differential Equations with Complex Eigenvalues

I think I might just be having trouble with formatting my answer, because I'm fairly sure my work is right up until this point. The question asks to find the general solution to $$X'= \begin{bmatrix}...
0
votes
0answers
17 views

Euler explicit and semi-implicit

I am given a simple dynamic system with an initial condition: $a(t) = 0.9 - 0.1v(t)$ $v(0) = x(0) = 0$ I want to calculate $x(1)$ with a time step of $\Delta t = 1$ using Euler explicit and semi ...
0
votes
0answers
22 views

Nonlinear equations algorithm - Newton method

Some time ago I posted a question regarding the simple case of finding the intersection point when I have only two functions, and with your help I found an answer. It was this case: $f(x) = a + \...
2
votes
1answer
76 views

A seemingly-trivial divisibility conjecture

While working on another problem, I stumbled on the following divisibility claim. Conjecture: No integers $a,b,c,d$ satisfy all of the following conditions: $a^2+b^2-c^2-d^2 = 2(ad-bc)-1$; $\gcd(ac+...