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.

learn more… | top users | synonyms (1)

1
vote
1answer
26 views

Set of linear equations with coefficients - solution using matrices

I have a set of linear equations: \begin{matrix} ax_{1}& {}+bx_{2}& {}+x_{3}& & =0\\ cx_{1}& {}+dx_{2}& &{}-x_{4} & =0\\ & {}-ex_{2}& ...
3
votes
1answer
43 views

periodic solution of $x''-\ (1-\ x^2-\ (x')^2)\ x'+x=0$

Assume differential equation $$x''-\ (1-\ x^2-\ (x')^2)\ x'+x=0$$ I want to discusse about non-constant periodic solution of it. Can someone give a hint that how to start to think. And does it have ...
2
votes
0answers
25 views

Interpretation of a 3 Variable System of Equations

I'm a high school student, and, of course, this week is finals week. For my Algebra 2 semester final, we have been permitted to take the test home and collaborate with others. This final can be viewed ...
2
votes
1answer
29 views

Using Lagrange multipliers to find the extrema of $f(x,y) = e^{2xy}$ subject to $x^2+y^2 = 16$

Find the maximum and minimum values of $f = e^{2xy}$ with respect to $x^2+y^2 = 16$. Using Lagrange multipliers, $\nabla f = \lambda\nabla g$. Therefore, the constraints are the following: ...
-5
votes
0answers
43 views

is this systems of equations solvable

i saw this equation posted yesterday and i wanted to ask if i could have help helping this kid solve it. he is in pre-algebra and i am in algebra so not much of a difference. i have tried to solve for ...
1
vote
3answers
57 views

Showing unstablity of differential equation.

Assume differential equation $$ x'=2x+y+x \cos t-y \sin t $$ $$ y'=-x+2y-x\cos t+y \sin t $$ Show that solution $(x(t),y(t))=(0,0)$ is unstable. Is there a non-trival solution such that ...
-1
votes
1answer
27 views

systems of equations with one inequality and exponents.

I have a systems of equations for a website that relies on the solution. I have just read up on the subject online but I still can't come to a conclusion. The equation is this: $$8000 \lt xy^5 \lt ...
0
votes
1answer
29 views

systems of equations with exponents?

I am building a website which will run on the equation specified below. I am in pre-algebra and do not have any idea how to go about this equation. my friends say it is a system of equation but I ...
1
vote
3answers
25 views

Finding number of integral solutions

I am really getting confused in this question. Number of integral solutions of the equation. $x_1x_2x_3x_4=770$ options- $2^{11}$ $2^{10}$ $4^4$ $5^5$ I attemtemted it by saying that ...
0
votes
3answers
79 views

Why does the determinant $D$, have to be $0$ for equation to have a solution?

Suppose $2\times2$ equation: $$ \begin{cases} a_1x + b_1y = c_1 \\ a_2x + b_2y = c_2 \end{cases} $$ We can make determinants: ...
3
votes
4answers
84 views

How to solve the system $x y^5=8000$ and $x y^4>4100$?

I need help getting this equation solved for a website I am building. I am pretty bad at math and am only in pre-algebra. I don't know how I would go about canceling out the ^5 and ^4 because I can't ...
0
votes
2answers
21 views

How many of each ticket were sold in one day?

Child tickets - $\$7$ Adult Tickets - $\$10$ Senior Tickets - $\$5$ Day one sold $678$ tickets for $\$5,812$ Day two sold $535$ tickets for $\$4,541$ How many of each ticket were sold on day one ...
0
votes
2answers
15 views

Solving systems of equations using matrices by row reduction

Solve the following system for $a$, $b$, and $c$: $$\begin{pmatrix}1 & -1 & 2\\2 & -2 & 2 \\ 3 & -3 & 2\end{pmatrix}\begin{pmatrix}a\\b\\c\end{pmatrix} = ...
1
vote
2answers
39 views

How to solve a linear system in matrix form using Laplace transform?

How to solve this linear system using Laplace transform? $$\mathbf X'(t)=\left[\begin{array}{r,r,r}-3&0&2\\1&-1&0\\-2&-1&0\end{array}\right]\mathbf X(t); ~~~~~~~~\mathbf ...
0
votes
2answers
48 views

Solution to a system of linear equations with an unknown matrix product

Consider the system of equations $$ Xy=Ab $$ where $X$ and $A$ are $m \times m$ invertible matrices and $y$ and $b$ are $m \times n$ matrices. The matrices $X$ and $y$ are unknown and the matrices $A$ ...
0
votes
1answer
22 views

Linear Systems of Differential Equations - Container Mixing Problem

So the questions goes something like this: I have two containers, 1 and 2. Pure water enters container 1 at a rate of 3 liters per minute, while the well-stirred mixture is leaving container 2 at the ...
2
votes
3answers
42 views

System of equations $x^2=y^3, x^y=y^x$

Solve the system of equations $x^2=y^3, x^y=y^x$ in positive real numbers. Taking $\ln$ of the second equation, we have $\ln x/x=\ln y/y$. This function is increasing in $(0,e)$ and decreasing in ...
1
vote
1answer
21 views

Finding the value of $y=b^2(3a^2+4ab+2b^2)$ if $a^2(2a^2+4ab+3b^2)=3$ and $a$ and $b$ are distinct zeros of $x^3-2x+c$

If $a$ and $b$ are distinct zeroes of the polynomial $x^3-2x+c$ and $$a^2(2a^2+4ab+3b^2)=3$$ $$b^2(3a^2+4ab+2b^2)=y$$ Evaluate $y$ I tried for many hours but couldn't solve this question. ...
0
votes
3answers
43 views

find x again in equation

I asked a similar question but I wanted to be sure understand. I have to find $x$ in the equation $$x^2=-2x-1$$ I go to left and get $$x^2+2x+1$$ Then I use a similar trick used in similar question ...
1
vote
0answers
18 views

Matlab Newton's Method Non-linear system

There is something wrong with this program and I cannot seem to find it. I am trying to calculate the solution of a non-linear system using Newton's method. Matlab keeps saying there is a problem with ...
0
votes
1answer
19 views

How to model function with unknown exponents?

I know the Cobb-Douglass function which describes the production quantity: $$Q(K, L) = A \cdot K^\alpha \cdot L^\beta$$ Also I do know multiple assignments of K ...
1
vote
5answers
37 views

Solving system when terms have both variables

$$x^3-3y^2x=-1$$ $$3yx^2 -y^3=1$$ This was the real part and imaginary part on a previous question I asked, instead of the system it was easier to just use polar coordinates to solve, but if this was ...
3
votes
2answers
21 views

For what values of a will the system have a unique solution, and for which pair of values (a,b) will the system have more than one solution

consider the following linear system $$x+2y+2z=1\tag{1}$$ $$x+ay+3z=3\tag{2}$$ $$x+11y+az=b\tag{3}$$ in matrix form $$\pmatrix{1&2&2&1\cr1&a&3&3\cr1&11&a&b\cr}$$ ...
2
votes
3answers
34 views

Solving $z^3=-1+i$

First, is there a better way than using x+iy and solving the system? I tried letting $z=e^{i3\theta}$ and using the cosine and i*sine way but I don't see how that can equal -1 and i at the same time, ...
1
vote
0answers
34 views

Reducing a system of differential equations

Let $\mathbf F$ be a system of 1st order differential equations in $n>3$ variables $$\mathbf{F} : \mathbb{R}^n \to \mathbb{R}^n$$ $$\frac{d\mathbf{u}}{dt} = \mathbf{F}(\mathbf{u})$$ such that ...
0
votes
1answer
24 views

Solving numerically a non-linear equation.

How is the more appropriate numerical method to solve the equation $$\cos(2\pi x)+\cos \left(\frac{2\pi N}{x}\right)=2,$$ for a given $N$? Notice that if $N \in \mathbb{Z}$, then $x\mid N$.
2
votes
1answer
83 views

Determine when the system has a) no solution, b) 1 solution and c) infinitely many solutions

This question is not for an assignment, it was on the midterm and I am interested in figuring out how to solve it before the final exam. cheers, Determine when the system has a) no solution, b) 1 ...
0
votes
0answers
23 views

Solving system of inequalities, with solution in only natural numbers, with priority on variables

If I have the equations $27a+30b+33c+36c \geq x$ $a+b+c+d=4$ and want to solve them using only natural numbers (including 0) for both $x=131 $ and $x=142 $ preferably but not necessarily with ...
0
votes
1answer
26 views

System of Non-Linear ODE

Does anyone have any clue of how to find an analytical solution for the following system: $$ \frac{dF_1}{dt}=(p+qF_1-rF_2)(1-F_1) $$ $$ \frac{dF_2}{dt}=vF_1(1-F_2) $$ $p$, $q$, $r$ and $v$ are ...
2
votes
0answers
33 views

Solving a system of two linear PDE: $u_x+v_x +u_y=0$ and $v_x+u_y-{1\over 2} v_y=0$

trying to solve the following cauchy problem: $$u_x+v_x +u_y=0\\v_x+u_y-{1\over 2} v_y=0\\u(x,0)=1-x,v(x,0)=x$$ my solution is: 1. multiply each equation by $t_1,t_2$ and sum the two equations like ...
0
votes
2answers
45 views

Simple system of nonlinear ordinary differential equations

I'm trying to solve a system of ODEs of the form: $$\frac{d^2a}{dt^2} = \frac{-1}{(a-b)^2}$$ $$\frac{d^2b}{dt^2} = \frac{+1}{(a-b)^2}$$ and with the following boundary conditions: $$a'(0) = 0$$ ...
0
votes
1answer
30 views

Easy system of equations?

Given the system of equations find $ v_3,v_4$ . If you only know the value of $ v_1,v_2$ $p_0+p=p_1$ $p_1+p=p_2$ $p_0+2p=p_3$ $p_3+p=p_4$ $p_1v_1 = p_2v_2 = p_3v_3 = p_4v_4$ Came to the equations when ...
3
votes
3answers
65 views

Ratio between two numbers is 6:7 and the difference between them is 10. What are the two numbers?

I know the numbers are $60$ and $70$ but I got that by trial and error. Is there some other more logical way to do this problem?
0
votes
3answers
31 views

Chinese Remainder Theorem Finding the Modulo

Find numbers $t,u,v$ so that $33t+2 = 20u+13 = 29v-1 $ This is a Chinese Remainder Theory problem, but the problem I am having is finding what are the appropriate modulo. I figure it is easiest to ...
0
votes
0answers
17 views

Prove this relation

Solve this: $y^2+2=x^3$ or Prove that $y^2+2=x^3 => (x,y)=(3,\pm 5)$ I know that it could be obvious to some of you by trial and error but I need a methodical approach. Thanks in advance!
0
votes
2answers
16 views

Intuition for using vectors in sale related problems

I am reading Linear Algebra from David Lay's book. He gives one example to showcase use of linear combination of vectors : I understand the solution, but I am completely clueless about how to ...
0
votes
0answers
41 views

If $x^a + x^b = x^c + x^d$ how do $a ,b , c , d$ relationship are?

I used to solved these equation style and it's accidentally found an answer from matching $a, b, c,$ and $d$ relationship when $x^a + x^b = x^c + x^d $ (I assume that $ab = cd$) and found that's ...
2
votes
3answers
30 views

Solutions for a system of congruence equations

I have a system $$ \begin{cases} x \equiv 7 \pmod{15} \\ x \equiv 14 \pmod{33} \end{cases} $$ How can I show that the system does not have any solutions? I know that the first implies that $x = ...
1
vote
1answer
17 views

Solving a pair of equations across a data set

I have the following pair of equations: $a = x\cos(k) - y\sin(k),\ b = x\sin(k) + y\cos(k)$ I know that all variables but $k$ are in the set $\mathbb{N}^0$. Given the above, if I know the value of ...
0
votes
1answer
19 views

Strictly positive linear combination of vectors

I have a matrix S of size $m \times n$. How to find a linar combination of the $n$ column vectors of the form: $x = col(1) + \sum_{i=1}^{i=n}{\lambda_i col(i)}$ such that all entries of $x$ are ...
1
vote
1answer
48 views

Can the equation $\mathbf{Av}=\mathbf{b}$ be solved as $\mathbf{v}=\mathbf{A}^{-1}\mathbf{b}$?

Say I have a $3\times 3$ matrix called $\mathbf A$ and a column matrix vector $\mathbf v$ and another column matrix vector $\mathbf b$. If I have the equation $\mathbf{Av}=\mathbf{b}$ where I know ...
0
votes
1answer
37 views

Faisablity of $Ax=b$

Be the following equation $Ax=b$ where $A$ and $b$ have entries over $\mathbb{N}$. $A$ is a full rank matrix of size say $m \times n$. 1) How to check if the equation admits a strictly positive ...
0
votes
3answers
35 views

How to solve greater & less / inequal equation

Two farmers, Eric and Josef where talking. "How many sheeps do you have?" asked Eric. "If I divide my sheeps in $2, 3, 4, 5,$ or $6$ groups, there will always be 1 sheep left." Josef answered. How ...
0
votes
1answer
25 views

Existance of solution of $Ax < b$

How to check if the inequality $Ax < b$ admits at least one solution. Entries of $A$, $x$ and $b$ are taken in $\mathbb{Z}$
0
votes
1answer
40 views

Solve the system of equations for x and y

Solve the system of equations for $x$ and $y$: $$ \left(\frac{x}{8-2y}\right)^2 - \left(\frac{y}{-4}\right)^2=4 \\ \frac{x}{8-2y} + \frac{x}{-2}=1 $$ I used Lagrange multipliers with multiple ...
2
votes
1answer
32 views

Solving a non-linear system of equations

Studying for finals I have come across a result that I understand how the system is derived but I cannot solve the system. I feel like this should be trivial, but I do not know where to go. Through ...
0
votes
1answer
28 views

Converting from Non-basis coordinates to XYZ. Solving system of equations. Error volume

I have multiple points in 3D space. Each point has the distances to 3 points. Those 3 points are: (50,0,0) (0,50,0) (0,0,50) Lets call those distances $dx,dy,dz$ I want to find $x,y,z$ of those ...
0
votes
0answers
32 views

Find constants α,β,γ,δ such that the limit exists

I have to find $\alpha,\beta,\gamma,\delta \in \Bbb R $ such that $$\lim \limits_{x \to 1} f(x) \in \Bbb R$$ where $$f(x) = \begin{cases}\frac{\alpha x^3-(\beta+\gamma)x-(\alpha+\delta)}{(x-1)^2} ...
2
votes
2answers
61 views

solutions to nonhomogeneous system of differential equations with general solution already known

Let's say we have the general solution to $X' = A(t)X$, where $X=(x_1, x_2)^T$. How do you find the general solution to the system $X'= A(t)X + b(t)$ where $b(t)$ is a $2 \times 1$ matrix with two ...
0
votes
1answer
21 views

One solution of a diophantine system

How to find one solution of $Ax = b$, where $A$ is a $(m, n)$ matrix and $x$ a vector of size $(n, 1)$. $A$, $x$ and $b$ are matrices of integers entries. How to check whether is a solution exists?