# 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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### Steps to solve this system of equations: $\sqrt{x}+y=7$, $\sqrt{y}+x=11$

I want to solve this system of equations, I have been out of Maths for a long!! $$\sqrt{x}+y=7$$ $$\sqrt{y}+x=11$$ Just wondering easiest step to find values for $x$ and $y$ from the above ...
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### Three-variable system of simultaneous equations

$x + y + z = 4$ $x^2 + y^2 + z^2 = 4$ $x^3 + y^3 + z^3 = 4$ Any ideas on how to solve for $(x,y,z)$ satisfying the three simultaneous equations, provided there can be both real and complex ...
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### Is there a simpler approach to these system of equations?

I recently came across the following system of equations: $$x + y + z = 1 \\ x^2 + y^2 + z^2 = 2 \\ x^3 + y ^3 + z^3 = 3$$ And I have two questions: One, is there a way to prove or disprove ...
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### System of $24$ variables

Assume that $a_1, a_2,\ldots, a_{24}$ satisfy $$a_1+a_2+\ldots+a_{24}=26$$$$a_1^2+a_2^2+\ldots+a_{24}^2=26$$$$\vdots$$$$a_1^{24}+a_2^{24}+\ldots+a_{24}^{24}=26$$ Find $a_1a_2⋯a_{24}$. How do I solve ...
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### Complex numbers system of equations problem with 5 variables

Let $z_0$,$z_1$,$z_2$,$z_3$ and $z_4$ such that $z_i\in C$ that hold: $$(1)|z_0|=|z_1|=|z_2|=|z_3|=|z_4|=1$$ $$(2)z_0+z_1+z_2+z_3+z_4=0$$ $$(3) z_0z_1+ z_1z_2+z_2z_3+z_3z_4+z_4z_0=0$$ Prove that ...
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I have the 7 following reccurence relations: $A_n = B_{n-1} + C_{n-1}$ $B_n = A_n + C_{n-1}$ $C_n = B_n + C_{n-1}$ $D_n = E_{n-1} + G_{n-1}$ $E_n = D_n + F_{n-1}$ $F_n = G_n + C_n$ $G_n = E_n + ... 0answers 164 views ### When do two integral superellipses have 'nice' intersections? A recent question posed the nonlinear system \begin{cases} 3x^3+4y^3=7\\ 4x^4+3y^4=16 \end{cases} for real$(x,y)$and asked for the sum$x+y$. As noted by commentary in the question, this regrettably ... 2answers 4k views ### Find the value of k, (if any), for which the system below has unique, infinite or no solution. [duplicate] The system of equations are:$\begin{cases}x+y+kz = 1\\x+ky+z=1\\kx+y+z=1\\ \end{cases}$I am looking to finding values of$k$, for which this system has either no solutions, infinite many solutions ... 3answers 277 views ### Show that: a)$X^{-1}(t)$is bounded in$[\beta,\infty)$. b)No system solution approaches zero solution when$t \rightarrow \infty.$Let a system$x' = A(t)x$and suppose there are values positives$k, \beta$such that a positive fundamental matrix$X(t)$satisfies$\|X(t)\| \leq k$,$t \geq \betaand $$\liminf_{t \rightarrow \... 3answers 162 views ### How was the determinant of matrices generalized for matrices bigger than 2 \times 2? How was the determinant of matrices generalized for matrices bigger than 2 \times 2? I read a book a very long time ago where it said something like this: Given a system of two equations with two ... 6answers 126 views ### Solve the system of equations: a+b+c=2, a^2+b^2+c^2=6, a^3+b^3+c^3=8 [closed] If we have \begin{cases} a+b+c=2 \\ a^2+b^2+c^2=6 \\ a^3+b^3+c^3=8\end{cases} then what is the value of a,b,c? 1answer 619 views ### Method of characteristics for a system of pdes I can do parts a) and b) as follows \begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1\end{pmatrix}\frac{\partial}{\partial{}x}\begin{pmatrix} u \\ v \\ w\end{pmatrix}+\begin{pmatrix} 1&... 1answer 148 views ### Roots of unity and a system of equations by Ramanujan Is it immediately apparent that the solution to the system of equations,$$\begin{aligned} x_1^2 &= x_2+2\\ x_2^2 &= x_3+2\\ x_3^2 &= x_4+2\\ &\vdots\\ x_n^2 &= x_1+2\\ \end{... 1answer 118 views ### Solutions to simultaneous Diophantine equations2y^2-3x^2=-1$and$z^2-2y^2= -1$I am looking for integer solutions for the following set of equations:$2y^2-3x^2=-1z^2-2y^2= -1$I know that there are the solutions (1,1,1) and (-1,-1,-1) for this set of simultaneous ... 4answers 116 views ### Solve the System of Equations in Real$x$,$y$and$z$Solve for$x$,$y$and$z\in \mathbb{R}if \begin{align} x^2+x-1=y \\ y^2+y-1=z\\ z^2+z-1=x \end{align} My Try: ifx=y=z$then the two triplets$(1,1,1)$and$(-1,-1,-...
Which two numbers when added together yield $16$, and when multiplied together yield $55$. I know the $x$ and $y$ are $5$ and $11$ but I wanted to see if I could algebraically solve it, and found I ...
I am seeking a general solution to a system of non linear equations with a specific pattern: Order 1: $$x_0 = a^2 + b^2$$ $$x_1 = 2ab$$ Order 2: $$x_0 = a^2 + b^2 + c^2$$  x_1 = 2ab + 2bc \$...