# 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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### What values of 'a' and 'b' would create a unique, no, and infinite solution(s)?

The following problem has really troubled me: I have row reduced it, so now it looks more like this: How do I really figure out what values of a and b would create infinitely many solutions, no ...
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### System of equations premutations

When I permutate a,b,c,d,e to the left the value on the right side changes by 1. Can I make some use of this information to solve the following system of equations? I don't really know have to solve ...
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### System of equations symmetric

How do I solve the following system of equation? $$xyz = x+y+z$$ $$xyt = x+y+t$$ $$xzt = x+z+t$$ $$yzt=y+z+t$$ I have no idea how to do.
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### Systems of ODEs

I want to solve a system of ODEs of the following type: $$\large\frac{d\phi_{i}}{dt} = {\mu_{i}}^2\phi_{i} + \sum_{j=1}^{N}a_{ij}\phi_{j}$$ There were IMSL/Visual Numerics routines such as DMOLCH, ...
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### How can I solve this hard system of equations?

Solve the system below \begin{align} &\sqrt {3x} \left( 1+\frac {1}{x+y} \right) =2\\ &\sqrt {7y} \left( 1-\frac{1}{x+y} \right) =4\sqrt{2} \end{align} Frankly I am disappointed, ...
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### Is there an adjective to describe systems of equations which is neither underdetermined nor overdetermined?

What might I call a system of equations in which the number of equations equals the number of free variables? In other words, if a system of equations is neither underdetermined nor overdetermined, ...
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### Preconditioner operator

hope you can help me. I have learned that a preconditioner is a matrix $P$ such that when it is applied to a system $A \mathbf{x} = \mathbf{b}$, the spectral properties of the matrix $P^{-1} A$ are ...
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### simultaneous equations help needed

I think of two numbers, x and y. When I add them together I get 5 and when I find the difference I get 13. What numbers did I think of? I need to know how to write this down in simultaneous equation ...
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### System of linear congruence when not relatively prime

I am new to Abstract Algebra and understand how to solve when the mods are relatively prime, but I am struggling when they aren't relatively prime. I have a system of of linear congruences that I ...
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### number of real triplets $(x,y,z)$ in system of equations

Total number of real triplets of $(x,y,z)$ in $x^3+y^3+z^3=x+y+z$ and $x^2+y^2+z^2=xyz$ $\bf{My\; Try::}$ Let $x+y+z=a$ and $xy+yz+zx=b\;,$ Then $(x+y+z)^2-2(xy+yz+zx)=xyz\implies a^2-2b=xyz$ And ...
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### Existence of solution for nonlinear (algebraic) equations.

Let $f_1(x_1,\cdots,x_n)=0$, $\vdots$ $f_n(x_1,\cdots,x_n)=0,$ be a nonlinear equation. Is there a condition on $f_1,\cdots,f_n$ under which this equation has a solution? Thanks for your help.
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### First integrals for solving system of ODEs

Assume a problem $$\begin{cases} \frac{\mathrm{dx}}{\mathrm{dt}} = \frac{y}{x-y}, \\[2ex] \frac{\mathrm{dy}}{\mathrm{dt}} = \frac{x}{x-y}. \end{cases}$$ Additionally, $x = x(t)$ and $y=y(t)$. ...
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### Using augmented matrices to find a number

There's this system of equations $$(8 − a)x_1 + 2x_2 + 3x_3 + ax_4 = 2$$ $$x_1 + (9 − a)x_2 + 4x_3 + ax_4 = 1$$ $$x_1 + 2x_2 + (10 − a)x_3 + ax_4 = 2$$ $$x_1 + 2x_2 + 3x_3 + ax_4 = 2$$ Now I have ...
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### Algebraic system of equations problem

Solve the follow system of equations: $$x+y+z=5$$ $$\frac{1}{xy}+\frac{1}{yz}+\frac{1}{xz}=5$$ $$x^3+y^3+z^3=53$$ Thanks for any help.