# Tagged Questions

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

How do you solve a system of equations with e^x. For example
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### 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, ...
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### 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 $6.75$ ...
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### 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 ...
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### 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 ...
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### 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!
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### 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 ...
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### 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 $X$ ...
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### 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 ...
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### 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.
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### 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. (...
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### 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 ...
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### 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 , ...
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### 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) -...
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### 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 ...
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### 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.
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### 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 ...
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### 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 $x$.
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### 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 ...
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### 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] & \...
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### 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 ...
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### 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}...
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 ...