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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1
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1answer
14 views

Why do the 1's in Gauss Jordan RREF need to be along main diagonal and not other diagonal?

I've practiced G-J elimination and understand most of the algorithm insofar as it represents the different manipulations one can apply to a system of equations. However, when we're talking about ...
-5
votes
1answer
24 views

For what values of a constant does the system have: No solution; More than one solution; Unique solution [on hold]

Consider the linear system . For what values of a does the system have: a) No solution; b) More than one solution; c) Unique solution It should be answered by augmented matrix.
-2
votes
1answer
38 views

Trouble with two equations with 4 unknowns [on hold]

I was wondering if I could receive assistance for the following system: $$\begin{cases}(x/a)^{3.2}+(y/b)^{3.2}=1\\ a/b = 174.1/86\end{cases}$$ I'm looking for integer solutions or how to find them ...
2
votes
0answers
8 views

Function intersecting 3 points & deriviate is positive for a range of x values

Thank you for taking the time to help out on this question. I'm looking for a function that intersects 3 points, and a derivative for every value of x between x=0 and x = 365 where dy/dx >= 0. My ...
0
votes
0answers
15 views

System of equations and chain rule

I have this system $\nabla b(z_1,\ldots,z_m)=\psi^\prime(\theta)\nabla\theta(z_1,\ldots,z_m)$. Where we have $\theta(z_1,\ldots,z_m)=\sum_i^m z_i$ and $b(z_1,\ldots,z_m)$=$\sum_i^m z_i^2$ What is ...
0
votes
2answers
19 views

Multistep Equation with Square Root Confusion

Alright, so I have $4 * \sqrt{3} = \sqrt{x}$ So I squared the entire equation to get $$16 * 3 = x$$ $$x = 48$$ Is this correct? Or do I only square the $\sqrt{3}$ part on the left side of the ...
0
votes
1answer
13 views

Discrete convolution equation

Let $x_1 = (x_1^k)_{k =-\infty}^{+\infty}$, $x_2 = (x_2^k)_{k=-\infty}^{+\infty}$, $x_3 = (x_3^k)_{k=-\infty}^{+\infty}$ be three sequences of real numbers such that $x_j^k = 0$ for $k < -m_j < ...
1
vote
1answer
37 views

Is it possible to solve this system of equations? [duplicate]

Consider a system of equations given below: $ p_1 + p_2 + p_3 + p_4 + p_5 = 1 $ $ x_1*p_1 + x_2*p_2 + x_3*p_3 +x_4*p_4 =0$ $ x_1^2*p_1 + x_2^2*p_2 + x_3^2*p_3 +x_4^2*p_4 =1$ $ x_1^3*p_1 + ...
0
votes
1answer
8 views

tridiagonal matrix with a corner entry from upper diagonal

I am trying a construct a matlab code such that it will solve an almost tridiagonal matrix. The input I want to put in is the main diagonal (a), the upper diagonal (b) and the lower diagonal and the ...
0
votes
2answers
23 views

Is it possible to have a system of equations that all equal 0, and not have each unknown's value be 0?

I'm doing about a 2 hour long homework assignment where by hand I must construct a 10x10 matrix representing a system of equations. Based on the pattern I'm seeing, I can tell all of the equations ...
1
vote
0answers
32 views

Solving a system of two nonlinear functions with three variables [on hold]

Say I have the two two-dimensional, three-variable equations F and G that must be graphed on the three-dimensional plane. How can I find a one-dimensional,three-variable equation H that describes all ...
-5
votes
2answers
30 views

Ticket price word problem - Simultaneous equations [on hold]

Jen has been pricing speed-pass train fares for a group trip to NY. Three adults and four children must pay $\$101$. Two adults and three children must pay $\$71$. Find the price of the adults ticket ...
5
votes
0answers
71 views
+50

How prove this systems-equation has least two postive integers solution

Show that: for any $k\ge 100,(k\in N^{+})$, there exsit $p\in N^{+}$, such $$\begin{cases} a+b+c=k\\ abc=p\\ a>b>c \end{cases}$$ has at least two postive integers solution $(a,b,c)$ ...
1
vote
2answers
37 views

Solving simultaneous PDEs

Given the equations (1):$$\frac{\partial u}{\partial t}+g\frac{\partial \eta}{\partial x}=0$$ and (2):$$\frac{\partial\eta}{\partial t}+H\frac{\partial u}{\partial x}=0$$ can we combine the two ...
0
votes
1answer
23 views

Matrix with given row and column sums

Let $N$ and $K$ be two given integer numbers different from zero. Let $S_n$ with $n=1,...,N$ and $C_k$ with $k=1,...,K$ strictly positive integer numbers such that $$ ...
-2
votes
0answers
17 views

Find the values of a and b so the system shown has the solution (2,3). Does the system have any other solutions? Explain. [on hold]

12x-2by=12 3ax-by=6 Find the values of a and b so the system shown has the solution (2,3). Does the system have any other solutions? Explain.
2
votes
4answers
35 views

Simultaneous Quadratic Equations: $x^2 + y ^ 2 - 2 x + 6y - 35 = 0$ and $2x + 3y = 5$

I've been given the task to simultaneously solve: $$x^2 + y ^ 2 - 2 x + 6y - 35 = 0$$ $$2x + 3y = 5$$ I've tried applying the substitution method by reordering the second equation to both $x$ and ...
1
vote
1answer
19 views

Solution of system of equations in prime fields

In 'Algebra', Artin writes that the system of equation: $$8x+3y = 3$$ $$2x+6y = -1$$ have no solutions in $\mathbb{F}_2$ and $\mathbb{F}_3$ as the determinant (of the coefficient matrix) evaluates ...
1
vote
1answer
36 views

System of ODEs obtained by using the method of characteristics for $u_x + 2u_t - 4u = e^{x+t}$

I have a question which requires me to use the method of characteristics in order to solve the PDE $u_x + 2u_t - 4u = e^{x+t}$. This results in the system of ODE's $\frac{dx}{dr} = 1 , \frac{dt}{dr} ...
0
votes
1answer
98 views

Solve the system $ x \lfloor y \rfloor = 7 $ and $ y \lfloor x \rfloor = 8 $.

Solve the following system for $ x,y \in \mathbb{R} $: \begin{align} x \lfloor y \rfloor & = 7, \\ y \lfloor x \rfloor & = 8. \end{align} It could be reducing to one variable, but it is ...
0
votes
2answers
35 views

Simple trigonometrical equations

I'm having difficulties in solving the simultaneous equations $$ \begin{cases} \sin(x+y)=\frac{1}{\sqrt{2}}\\ \cos(2x+y)=\frac12 \end{cases} $$ for $0^{\circ}\le x,y\le 90^{\circ}$. The answer is ...
1
vote
2answers
62 views

Analog clock with same hands - sometimes one can't tell time [duplicate]

There is an accurate analog clock, however both hands are the same size and shape. How many moments during a day a person can not conclude current time from the position of the hands? This is from a ...
0
votes
1answer
13 views

Differential system, a matrix with eigenvalue

Let's say that we have $n$ differential equations written in the form: $x'(t) = Ax(t) + v \exp(\lambda t)$, where $v$ is the eigenvector of $A$ such that $A v = \lambda v$ and $A$ is a $n \times n$ ...
0
votes
2answers
31 views

Can the following system be solved symbolically/analytically?

I have the following system of equations with variables $a,m$, and I'm wondering—can this system be solved symbolically/analytically? \begin{align} m &= 100 + \frac{ \left( 200 ...
2
votes
0answers
42 views

How to find whole number answers in systems of square root equations

Given the following 4 equations, can you find 4 whole number answers using whole number variable inputs? $x,y,z$ where $x>y>z$ $Eq 1 = (x^2-2xy+y^2-2xz+z^2)^{\frac{1}{2}} $ $Eq 2 = ...
0
votes
1answer
50 views

Gauss Method to show [closed]

Could you please give me the way to solve this problem Using Gauss method to show if $x ≠ y + 1$ then $$ \sum_{i=0}^n (x-y)^i = \frac{(x-y)^{n+1}-1}{x-y-1}. $$
0
votes
0answers
19 views

How do I solve massive system of equations (with lots of variables) quickly?

Just wondering how to solve system of equations involving 3+ unknowns quickly. In my math class, we're given questions like these which involve solving huge system of equations on a time limit, ...
0
votes
2answers
36 views

Find $x(t)$ and $y(t)$ which satisfy the following differential equations

Find $x(t)$ and $y(t)$ which satisfy $3\dot x + \dot y +5x-y=2e^{-t}+4e^{-3t}$, $\dot x + 4\dot y -2x+7y=-3e^{-t}+5e^{-3t}$, subject to $x=y=0$ at $t=0$. This is how I tried it: If we multiply ...
0
votes
2answers
130 views

$10$ Equations in $10$ variables

$x + y + z + u + v = 2$ $xp + yq + zr + us + vt = 3$ $xp^2 + yq^2 + zr^2 + us^2 + vt^2 = 16$ Similarly, $xp^3 + ... + vt^3 = 31$ Power $4,$ that is $xp^4 +... + vt^4 = 103$ Power $5 = 235$ Power ...
1
vote
3answers
56 views

Solve these equations simultaneously (trig)

Solve for $ x,y: $ \begin{equation}\cos x -\cos(x+y) = 0 \end{equation} \begin{equation}\cos y -\cos(x+y) = 0 \end{equation} The answers are $(0, 0), (\frac{2\pi}{3}, \frac{2\pi}{3})$. I get ...
0
votes
0answers
27 views

Solution of a general linear system of equations: 4-term n-equations

I have the following system of equations.... $$y_1 = c_{11} \cdot x_{11} + c_{12} \cdot x_{12} + c_{13} \cdot x_{13} + c_{14} \cdot x_{14}$$ $$y_2 = c_{21} \cdot x_{21} + c_{22} \cdot x_{22} + ...
0
votes
0answers
9 views

Can this equation have an explicit solution?

Given $n > 0$, $0 \leq i \leq n$ is an integer, $D = diag(d_1, \dots, d_n)$ is positive definite, $e_i$ is the $i$th column of a $n \times n$ identity matrix, $u \in R^n$ such that $B = D + u * ...
1
vote
0answers
32 views

Rank of a matrix with parameters

I have the following matrix: $$\begin{pmatrix} b+3 & a & 4 & -2b-1\\ b & -3 & 5 & -6\\ -1 & 1 & 2a+1 & 1-a \end{pmatrix}$$ How can I determine the rank for ...
0
votes
1answer
23 views

System of linear equations where unknowns can only be +1 or -1

I have a system of linear equations, in which the unknowns can only take 2 integer values: +1 or -1. The linear system is $$ Ax = 0 $$ Matrix A is shown below with dimension (3 x 14): $$ ...
2
votes
0answers
27 views

How to solve the equation $Au+Bv=C$

How do I solve $Au+Bv=C$ Where $A$ and $B$ are constant known matrices that are nxn, $C$ is a constant known nx1 vector while $u$ and $v$ are unknown nx1 vectors with the condition given that $u_i = ...
-1
votes
0answers
20 views

Number of escalator steps we can see [closed]

A man walks up an escalator that moves up and counts 50 steps. The next day he walks up the same escalator and counts 75 steps. If the second speed (in steps per time unit) is three times the first ...
3
votes
3answers
553 views

Question about a solution of a system of three non linear equations in three unknowns

Let $a$, $b$ and $c$ be positive real numbers such that $$ a + \frac{1}{b} = 3$$ $$b + \frac{1}{c} = 4$$ $$ c + \frac{1}{a} = \frac{9}{11} $$ then $$ a \times b \times c =?$$ I tried doing this ...
1
vote
0answers
18 views

How to diagonalise this pentadiagonal pseudo-Toeplitz matrix?

How can one diagonalise this N-by-N pentadiagonal matrix (where $r$ is some real constant)? $$ \tiny \begin{pmatrix} r^2 +r & -2r -1 & 1 & & & & & & ...
0
votes
0answers
33 views

Maximum of $x_1 - x_2 - x_3 + x_4 - 2x_5$ with some constraints

I have to find maximum of $x_1 - x_2 - x_3 + x_4 - 2x_5$ with constraints: $-x_1 +x_2 + x_3 = 2$ $x_1 + 2x_2 + x_4 = 10$ $x_1 - x_2 + x_5 = 4$ of course $x_i \ge 0$. From constrains I have: ...
1
vote
3answers
41 views

System of equations with radicals

Solve the system of equations (in $\mathbb R$): $$\begin{matrix} 2\sqrt[4]{\frac{x^4}{3}+4}=1+\sqrt{\frac{3}{2}y^2} \\ 2\sqrt[4]{\frac{y^4}{3}+4} = 1+\sqrt{\frac{3}{2}x^2} \end{matrix}.$$ This ...
0
votes
1answer
25 views

How can I solve this system of linear different equations?

Here's the system $$\frac d{dt} \begin{bmatrix} x \\ y \\ z \\ p_1 \\ p_2 \\ p_3\end{bmatrix} = \begin{bmatrix} 0 & A \\ B & 0 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \\ p_1 \\ p_2 \\ ...
0
votes
0answers
23 views

Classification of critical points for plane autonomous system

Okay so I've changed the 2nd order nonlinear ODE $$ x'' = a(x')^2 - ax' -ax $$ where a is a real constant, into $$ x' = y $$ $$ y' = ay^2 -ay - ax $$ I'm asked to verify the critical point (0,0). ...
0
votes
0answers
25 views

Solution to a ODE system using a power series

I'm certain the pattern the system creates is $$ A^kX(0) = \begin{pmatrix}2^k\\1\\2^k\end{pmatrix}\hspace{3pc} $$ Where A is a matrix created by the system and X(0) is a solution vector at t=0 Im ...
0
votes
0answers
25 views

How many solutions does this boolean equation system has?

How many solutions does this boolean equation system has? $$\left\{ ...
0
votes
0answers
28 views

A few questions about eignenvectors and the associated root vectors.

Let A be the matrix formed from the original system of equations and t is a repeated eigenvalue. I've noticed when solving problems containing eigenvectors of multiplicty >1 that when the ...
1
vote
1answer
32 views

System of linear equations with four unkowns

I have no idea how to solve this system of equation : $$\begin{align}u+v+w&=7 \\v+w+x&=-8 \\w+x+u&=5 \\x+u+v&=-10\end{align}$$ I usually use the addition/substraction method, but ...
0
votes
2answers
17 views

A simultaneous equation question

$38$ bottles of soda was consumed by $18$ women. Some took $2$ and others took $3$ . (A) How many women took $2$ sodas? (B) How many women took $3$ sodas? I thought I might use simultaneous equations ...
1
vote
2answers
42 views

Question on power, If 2x^2x^2x^2x… =4 Solve for x

I've seen this random example, in which can anyone give me clue how to solve for $ x $ here?
0
votes
0answers
17 views

Stuck on polynomial equation in optimization problem

I've been trying to solve an optimization problem, but I am completely stock on one step. I had the following Langrangian: $$\nabla\mathcal{L}(x,\lambda)= e\frac{\sum_{t\in I}e^t \Delta P(t)( x^t ...
0
votes
0answers
27 views

Perfect equilibrium - consumer, producer surplus

Inverse function of market demand for certain good is equal to $P=100-0.25Q$, inverse supply function is $P=20+0.55Q$. Calculate equilibrium price and quantity. Furthermore calculate consumer and ...