# Questions tagged [systems-of-equations]

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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### Solving a System of Equations with Zero Determinant Matrix

I'm trying to learn FEA and I'm going through the first example problem from the "Practical Stress Analysis with Finite Elements" book by Bryan Mac Donald. Here is the problem: Matrix ...
1 vote
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### Find all triplets $(a, b, c)$ of integers for which the following holds: $a^2 = bc + 1$ and $b^2 = ca + 1$. [duplicate]

Find all triplets $(a, b, c)$ of integers for which the following holds: $a^2 = bc + 1$ and $b^2 = ca + 1$. Attempt: First, I subtracted the two equations and obtained $(a-b)(a+b) = c(a-b)(-1)$. Now, ...
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### Finding the equation of a sine wave using two points and a tangent [closed]

I am trying to find a sine wave of form y=asin(b(x-c)) (a=/=0, b=/=0) that intersects the point (45, -25) with a slope of 1.55, and intersects the x-axis at x=52. using this information I made 3 ...
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1 vote
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### Finding a basis for an unknown-weights-and-balance puzzle?

I have a collection of unknown integer weights $w_1, \ldots, w_n$. I have a balance which I can use to weigh some pile of weights against some other pile to see which is heavier. Suppose I've done $n$...
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### How to Solve a Linear System of Equations with Absolute Values

I have encountered a system of linear equations that involves absolute values: \begin{align} |x + y| &= 1 \\ |x| + |y| &= 1 \end{align} I am having trouble finding resources or methods to ...
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### Prove $Max(L_1,L_2,L_3)\neq L_2$:$L_i=\frac{S_i^2}{n_i}+\frac{(S-S_i)^2}{n-n_i}$;$S=\sum S_i$;$n=\sum n_i$;$\frac{S_i}{n_i}>\frac{S_{i-1}}{n_{i-1}}$

I will state my question first, and after that, I will write how I arrived to it. You do not really need to see how I arrived to the question, but I just thought it would be rude not to explain that. ...
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### Existence of a linear equation in n variables

I have a question regarding a linear system that contains a single linear equation in n variables, that is, in the following form: $$a_1x_1 + a_2x_2 + \cdots + a_nx_n = b$$ Where $a_ 1, \cdots, a_n$ ...
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1 vote
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### How to solve, or quantify solutions of, polynomial equations in $\mathbb{F}_2[x,y]/\langle x^\mu - 1, y^\nu - 1\rangle$? [closed]

Suppose I was given an equation in $\mathbb{F}_2[x,y]$ under the identification $x^\mu = 1$ and $y^\nu = 1$ for some integers $\mu,\nu$, with some unknowns $c[x,y]$ and $d[x,y]$. For example: \begin{...
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### Maximise $xyz$ such that $x+xy+xyz=1$, $y+yz+xyz=2$, $z+zx+xyz=4$

$x, y, z$ are real numbers which satisfy the following: $$x + xy + xyz = 1$$ $$y + yz + xyz = 2$$ $$z + zx + xyz = 4$$ Then find the maximum value of $xyz$. I tried adding and subtracting a few ...
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1 vote