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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15 views

trying to solve a systems of equations with one inequality

I am trying to create a website that would run off this mathematical formula. I have tried to solve it but I got that there was no answer. I am only in pre-algebra and want a second opinion on if I ...
0
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2answers
36 views

Simultaneous equations with three parts

\begin{align*} 6a +24b +18c &= 168\\ 8a +28b +22c &= 208\\ 4a + 20b +20c &= 140 \end{align*} I've tried doing this multiplying so they cancelled out but I've always gotten decimal point ...
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2answers
28 views

System of equations with only variables

How do you solve a system of equations with variables on both sides? I have a problem solving this: $a + 3b = a + 2c$ $2a = b + 2d$ $c + 3d = 3a$ $2c = 3b$ I tried substituting $c$ for $1.5b$ but ...
3
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0answers
46 views

Writing ODE system with a complex variable

I'm looking at the system of ODEs: $$\begin{cases}\dot{x} = -y + kx + xy^2\\ \dot{y} = x + ky - x^2\end{cases}$$ I'm trying to introduce a complex variable $z = x+iy$ to write this as a single first ...
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2answers
33 views

System with more variables than equations!

Does the system of equations have a solution? : $a=3d$ $3b=3a+d+9e$ $3c=3b+e+9f$ $f+3c=0$ I was told by someone online that they solved it in terms of the variable $d$, in other words they got ...
0
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0answers
26 views

Can this equation be solved for i?

I was wondering if this equation could be solved for i, and if so how would that be done? $$c = \frac{k*[i*(i+1)^p]}{[(1+i)^p-1]}$$ Here's a working example: c = 121.96 i = 0.121 p = 6 k = 500 ...
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1answer
44 views

Difficult system of equations

Solve the indeterminate system: $a=3f$ $3b=10f+9g$ $3c=10f+10g+9h$ $3d=10f+10g+10h+9i$ $3e=10f+10g+10h+10i+9j$ $3e=-j$ EDIT: Please don't close it, I actually want to learn. This is a challenge ...
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2answers
167 views

what is the phase portrait of this system.

what is the phase portrait of this system. $$\begin{cases} \dot x_1&=-x_1+x_2\\ \dot x_2&=-x_2 \end{cases}$$ My work I have solved this, and I got the general solution as, ...
1
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1answer
62 views

How to manually solve this system of four equations?

Sorry for coming up with a "do-it-for-me"-question, but I can't think of another way to get help with manually solving the following system of four equations: $50=x*\cos(\beta)-y*\cos(\alpha)$ ...
3
votes
2answers
119 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 ...
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0answers
22 views

Finding the coordinates of the third point in a triangle using simultaneous equations

I have 3 circles A,B & C that touch each other at tangents. The centre points of these 3 circles are to be joined to create a triangle. I know the coordinates of 2 of the circles centre points ...
0
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0answers
34 views

Putting together a system of equations.

Someone helped me out with a problem a while back. Bout a year ago. But I still don't know how he derived the equation from or how he got it. I have two equations. $f/(f-n) = c$ $-nf/(f-n) = d$ We ...
2
votes
1answer
22 views

Solving a specific system of n non linear equations

I'm trying to solve a system of equations but I don't realy know how to tackle it. The equations all look as follows $a_1 x_1+b_1x_1x_2^2+c_1x_1x_n^2=d_1$ $a_2 x_2+b_2x_2x_3^2+c_2x_2x_1^2=d_2$ ...
0
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0answers
28 views

pound symbol in inequalities

a friend of mine has to solve some equations, but in some of them appears something like a pound symbol. Do you know what it means and how to solve it? or the teacher really lose his wit? Thank ...
0
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1answer
20 views

Explicit equation for recurrence relation

I have a recurrence relation: $A_{n} = -2A_{n-1} + 15A_{n-2}$ , with $a_{1} = 10$ and $a_{2} = 70$. This would be a linear homogenous recurrence relation of degree 2, right? Using the relation I ...
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1answer
51 views

System of equations ac = ax + by and ac^2 = ax^2 + by^2

I have these two equations: $$ ac = ax + by$$ $$ac^2 = ax^2 + by^2$$ I have to figure out $\mathcal x$ and $\mathcal y$ using $\mathcal a, \mathcal b, \mathcal c$ which are variables but not set ...
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1answer
20 views

Equations: Find $c,b,f$ if $c,b,f>0$

I am given $c^2+f^2+cf=49$, $c^2+b^2-cb=49$ and $f^2+b^2-fb=49$. Find $c,b,f$ if $c,b,f>0$ I couldn't do this by hand, please help All I can find out is that $c+f=b$.
2
votes
1answer
65 views

System of exponential equations

If $x,y,z \in \mathbb{R}$ and $$ \begin{cases} 2^x+3^y=5^z \\ 2^y+3^z=5^x \\ 2^z+3^x=5^y \end{cases} $$ does it imply that $x=y=z=1$?
3
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2answers
69 views

System of equations with 2 parameters

I have no idea how even to start! \begin{align*} (u^2+v^2)(u+v)&=15uv \\ (u^4+v^4)(u^2+v^2)&=85u^2v^2 \end{align*}
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2answers
25 views

simple systems of equations problem

Choose h and k such that the system has 1) no solution, 2) a unique solution, and 3) many solutions. Give separate answers for each part. x-3y=1, 2x+hy=k For 1) and 3), isn't that impossible? And ...
2
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1answer
38 views

To solve the system of Diophantine equations.

I decided to compile a single task and to record such a system. $$\left\{\begin{aligned}&xt+yw=az^2\\&xw-yt=br^2\end{aligned}\right.$$ $a,b - $ integers that are the problem. It is clear ...
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0answers
13 views

How to solve this kind of difference equation?

How to find $v_k$, $k=0,1,2,\dots$ such that $$v_k + \sum_{n=1}^{k} \frac{\alpha^n}{n}v_{k-n} + \sum_{n=1}^{k}\frac{\beta^n}{n}v_{k+n} = 0,$$ where $\alpha,\beta \in \mathbb{C}$. ($v_i=0$ for ...
2
votes
1answer
18 views

Logic supporting column operations on matrices

In matrices, we justify row operations by drawing parallels with solving a system of equations i.e.: 1.Interchanging rows = Interchanging equations \ 2.Adding one multiple of a row to another = ...
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0answers
15 views

Is there an efficent way to solve large systems of purely quadratic equations?

I have the following system of quadratic equations $$ b_1 = \sum_{k=1}^R x_{i_1, k} \ y_{j_1, k} $$ $$ \vdots $$ $$ b_p = \sum_{k=1}^R x_{i_p, k} \ y_{j_p, k} $$ where $i_1, \ldots, i_p \in ...
0
votes
2answers
66 views

Matrix invertible iff det(matrix)$\neq 0$?

When we want to find the inverse of the matrix $$\begin{bmatrix}a & b \\ c & d\end{bmatrix}$$ we're searching for a matrix $$\begin{bmatrix}x & y \\ z & w\end{bmatrix}$$ such ...
1
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0answers
18 views

Solve $b_1 e^{-a_1x^2}-b_2 e^{-a_2x^2}-b_3 e^{-a_3x^2}=0, \forall x$

Suppose, \begin{align*} b_1 e^{-a_1x^2}-b_2 e^{-a_2x^2}-b_3 e^{-a_3x^2}=0, \forall x \end{align*} Assume $a_1,a_2,a_3, b_1,b_2, b_3>0$ What are the possible values of $a_1,a_2,a_3, b_1,b_2, ...
1
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3answers
72 views

Equation system modulo prime

I have an excercise, it is to solve $$9\equiv_{p}8k_1+k_2$$ $$32\equiv_{p}6k_1+k_2$$ $$45\equiv_{p}11k_1+k_2.$$ $k_2$ is easily eliminated from the equations but I don't know how to proceed from ...
0
votes
1answer
62 views

$S_{1}\iff S_{2}$ in complex numbers

Let : $a_0 , a_1 , a_2 , b_0 , b_1 , b_2 \in \mathbb{C} $ : Show the following equivalence : $$\begin{cases} ( 1 + a_0 ) ( 1 + a_1 ) ( 1 + a_2 ) &=& ( 1 + b_0 ) ( 1 + j b_0 ) ( 1 + j^2 b_0 ) ...
1
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1answer
45 views

Solution of overdetermined polynomial system

Some of you will find this question pretty straightforward to answer, but I desperately need some help in solving a problem involving several equations and 2 unknowns, for an engineering application. ...
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votes
2answers
32 views

how many jelly beans did each girl have at first?

Martha and Mary had $375$ jelly beans in all. After Mary ate $24$ jelly beans and Martha ate $\frac 17$ of her jelly beans, they each had the same number of jelly beans left. How many jelly beans did ...
0
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0answers
32 views

Quention about the historical definition of determinant

$$ax+by = k_1\\cx + dy = k_2$$ If I want to solve for $y$ in the first equation: $$by = k_1 - ax\implies y = \frac{k_1-ax}{b}$$ Then substitute $y$ in the second equation: $$cx + d\frac{k_1-ax}{b} ...
1
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3answers
93 views

Let $p^3+q^3=4$ and $pq=2/3$ . Find $p+q$.

Let $p^3+q^3=4$ and $pq=\frac{2}{3}$ . Find $p+q$. A graphing calculator can find values of $p$ and $q$ numerically. As one can see from the graph below, the two solutions are approximately ...
0
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0answers
26 views

Substitution in a system of ordinary differential equations when terms of the same order derivative for different variables occur in the same equation

Let's say I have a differential equation such as: y'' - 2ty' + y = 0, y(0) = 2.1, y'(0) = 1.0 I can solve this (among other ways) by substitution and conversion ...
1
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1answer
31 views

A system of non-linear equations with a small parameter

Is there any way to solve analytically the following system of equations to the leading order in $\epsilon$: $$\left\{ \begin{array}{rcl} \mu^2 \phi_1 + \lambda \phi_1 (\phi_1^2 + \phi_2^2) + ...
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2answers
73 views

Solving a system of three simultaneous equations

Given the system $$ \begin{align*} -2x + ay - bz &= -4 \\ x + bz &= 2 \\ 2x + y + 3bz &= b \end{align*} $$ The question asks to find conditions on $a$ and $b$ that the system has no ...
1
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1answer
39 views

How can I solve a system of two equations, like $A + B = 13$ and $2D + B = 13$?

I am currently studying for my SSAT and this question appeared in my practice book: When $A + B = 13$ and $2D + B = 13$, what is the value of $D$? (A) 13 (B) 5 (C) -5 (D) -7 ...
1
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2answers
88 views

Solve system of 3 equations

$x+y+z=0$ $x^2+y^2+z^2=6ab$ $x^3+y^3+z^3=3(a^3+b^3)$ this is what i reasoned out so far; $xyz=a^3+b^3$ $x^2+zx+z^2=3ab$ $y^2+zy+z^2=3ab$ $x^2+xy+y^2=3ab$ $y^2=3ab+zx$ $x^2=3ab+zy$ ...
1
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1answer
28 views

Cannot figure out a second order lineary differential equation with initial values

I got the following question: Solve the following initial value problem: $y(0) = 0$, $y'(0) = 1$, $$y'' + 10y' + 25y = 0$$ So I started with getting the general solution: $$ y(x) = C_1e^{-5x} + ...
2
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0answers
26 views

$\sum (\sqrt{x_k-k^2}-k)^2=0$ implies $x_k=2k^2$?

Let $x_1,x_2,\ldots,x_n$ be reals numbers such that $$\sum_{k=1}^n k\sqrt{x_k-k^2}=\frac12\sum_{k=1}^n x_k$$ Find all possible $n$-tuples of solution. So, I got the following solution from ...
0
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3answers
34 views

How to solve this system of equations (Lagrange Multipliers)

I was doing a question on Lagrange multipliers and stucked when trying to evaluate the point. The system of equations that I can't solve is this: $$y^2-x^2+3x-3y=0$$ $$-y^2-yx+3y-xy=0$$ I just ...
1
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0answers
42 views

GMRES and Preconditioning

I am using GMRES to approximate the solution of a system of equations $Ax=b$, I am using a preconditioner $P$ to make GMRES converge faster. My question is how do I know if the preconditioner I am ...
4
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1answer
195 views

How to solve 29 coupled quadratic equations?

I have a set of 29 coupled quadratic equations, with 29 unknown variables. Can anyone offer any advice on how I could go about solving this? 3 days of staring at a wall has so far given me no ...
1
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1answer
29 views

What's the solution to this exponential system of equation?

What are the steps to solving a system of equations when $x$ and $y$ are exponents? But they have different base. Here is the problem. $5^x\times3^y=45$ $3^x\times5^y=75$
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4answers
83 views

Solving a homogeneous system of three ODEs with variable coefficients.

I am interested in solving the following system of ODEs: $$ \begin{pmatrix} x'(t) \\ y'(t) \\z'(t) \end{pmatrix} = a \begin{pmatrix} 0 & -B_2 & B_1 \sin \omega t \\ B_2 & 0& -B_1 ...
2
votes
1answer
83 views

Solving polynomial equation system to find three dimensional location

For an embedded systems project, I need to solve a system of equations. However, my algebraic skills are limited, and I am not able to solve it. This question consists of the following parts. The ...
2
votes
2answers
18 views

Finding the nth term in a recursive coupled equation.

I'm probably missing something simple, but if I have the recursive sequence: $$ a_{i+1} = \delta a_i+\lambda_1 b_i $$ $$ b_{i+1} = \lambda_2 a_i + \delta b_i $$ how would I find a formula for $a_n$, ...
3
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0answers
33 views

Why are equilibria so important?

In studying nonlinear systems of differential equations, unlike linear systems, it turns out that we are more interested in equilibrium points rather than general solutions themselves. I mean, look ...
4
votes
1answer
31 views

linearly independent and determinant

This question says a matrix $\begin{bmatrix}a & b\\c & d\end{bmatrix}$ where $a_{ij}$ are real numbers. I need to prove that $\det|A|=ad-bc\neq0 \iff $the columns are linearly independent. ...
1
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1answer
39 views

Solving the equations $x_1= 4 x_2$ and $x_3= 5 x_2$, with the sum of all three being $150$

Here is the problem. A set X is partitioned into subsets x1, x2, and x3. The number of elements in x1 is 4 times the number in x2. And the number in x3 is 5 times the number in x2. If n(x)=150, ...
2
votes
0answers
63 views

Impossible System of Equations

This is from a competition: DMM Olympiad, Ural State University P4 I don't understand what the question means exactly (the first part, i.e. "exclude $x$ or $y$ from..." part). Does it mean "write $x$ ...