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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2
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2answers
67 views

solve for three unknowns with two equations

Apple cost 97 dollars. Orange cost 56 and lemon cost 3. The total amount spent is 16047 dollars and total fruits bought is 240 and each one is bought atleast one. Calculate how many of each have been ...
1
vote
2answers
104 views

Determine the number of solutions of nonlinear system without solving.

$x^2-y^2+2y=0$, $2x+y^2-6=0$ I need to determine the number of solutions without solving it. There is a hint that a graph can help but I am still not sure how to go about this. Thanks
9
votes
6answers
583 views
+50

How find the value of the $x+y$

Question: let $x,y\in \Bbb R $, and such $$\begin{cases} 3x^3+4y^3=7\\ 4x^4+3y^4=16 \end{cases}$$ Find the $x+y$ This problem is from china some BBS My idea: since ...
0
votes
2answers
1k views

How to plot a phase portrait for this system of differential equations?

I beg your help.. I'd like the phase portrait for this system. I don't know how to use Mathematica/Matlab ... :( If anyone can make this portrait and post a print screen here, I would thank you ...
1
vote
0answers
63 views

When do two integral superellipses have 'nice' intersections?

A recent question posed the nonlinear system \begin{cases} 3x^3+4y^3=7\\ 4x^4+3y^4=16 \end{cases} for real $(x,y)$ and asked for the sum $x+y$. As noted by commentary in the question, this regrettably ...
2
votes
1answer
60 views

Infinite set of equations

Consider an infinite set of equations in an infinite number of variables, if every finite subset of equations has a solution, must the entire set of equations have one? Each equation contains a ...
2
votes
0answers
25 views

Solving systems of equations with trigonometric terms

I am trying to solve (or rather find the least squares solution for) a system of equations with trigonometric terms in them. The system consists of pairs of equations of the form $a_1 \cos\theta - ...
0
votes
1answer
38 views

How to solve the equations system?

I have a system of equations that I don't know how to solve. 1) $x = a - y$ ; 2)$ y = b \times sin(90 -z)$; 3) $z = \dfrac{(x - c )^2 }{b^2 \times e^2}$ $a, b, c, d$ and $e$ are known. How can I ...
2
votes
3answers
386 views

How to solve a system of three nonlinear equation in a simple way

Given the system: $$ \begin{cases} x^2y^2+x^2z^2=axyz & \\ y^2z^2+y^2x^2=bxyz &\\ z^2x^2+z^2y^2=cxyz \end{cases} $$ The solution could be gotten in a very tedious way. Is ...
0
votes
0answers
17 views

System of ODE's with varying times.

Sorry for the vague question, I wasn't really sure how to phrase this. This isn't for homework, it's a problem I am working on. It's been a long time since I've taken differential equations and I'm ...
2
votes
3answers
54 views

Given system of equations $a+b = 2, ab=4$ solve $a^2+b^2=?$ and $a^3=?$

I am trying to solve $a^2+b^2$ and $a^3$ given $a+b = 2, ab=4$. I have the key with the answers $a^2+b^2=-4$ and $a^3=-8$ but am wondering which steps to take to get to that answer. My understanding ...
0
votes
0answers
22 views

Solving system of equations

I have the following set of equations: $y = f(a,b)$ $a = f(y)$ $\dot{b} = f(b,y,\dot{y})$ which I like to solve for $y$. I was wondering if there is some numerical method which I can apply to ...
0
votes
0answers
13 views

Variable bounds of under-determined linear system

If I have a non-negative, under-determined linear system $\mathbf{Ax}=\mathbf{b}$ $\mathbf{x}\geq\mathbf{0}$ is there a fast way to compute the upper and lower bounds on values of each element of ...
0
votes
4answers
53 views

solving the system

solve the system : $$ y+|x-2|=3 $$, $$ |x+y|= m $$ graphicly when $m$ equals $6$. I can easily (realtively) skecth the first graph , however, how the bloody hell do you sketch $|x+y|= 6$??
0
votes
0answers
45 views

Predator Prey Equation

The Predator-Prey Equation is outlined by the following equation: $$\left\{ \begin{array}{l} \frac{dx}{dt}=\alpha x-\beta xy \\ \frac{dy}{dt}=-\gamma y+\delta xy \end{array} \right.$$ Can someone ...
3
votes
1answer
84 views

how to solve these equation?

For $a , b , x , y$ are members of $\mathbb{R}$ If $ax+by=3\\ax^2+by^2=7\\ax^3+by^3=16\\ax^4+by^4=42$ then $ax^5+by^5=?$ a lot of thanks for all comments
1
vote
0answers
20 views

Removing parametrization from a system of equations

Consider the following system : $$ \begin{aligned} \frac{d^2t}{d\lambda^2} &= -f\left(t\right)\frac{d t}{d \lambda}\frac{d t}{d \lambda} -A\frac{d g\left(t,x\right)}{d \lambda}\frac{d t}{d ...
1
vote
3answers
25 views

Iterative Equation Problem with Constraints

I was given a programming riddle recently. It was eluded to that there is an equation, but I was told that finding the equation was not the goal, and that writing a simple program was the goal. I ...
1
vote
1answer
232 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
0
votes
0answers
17 views

Matlab: solve system of equations using substitution

Suppose I want to solve a system of equations $F(x)$ which is shown as below: $x_1^3+1=0$ $x_1+x_2=0$ I want to substitute $x$ by $x_1=2y_1, x_2=3y_2$. Then the original system is transformed to ...
5
votes
4answers
74 views

Solve the System of Equations in Real $x$,$y$ and $z$

Solve for $x$,$y$ and $z$ $\in $ $\mathbb{R}$ if $$\begin{align} x^2+x-1=y \\ y^2+y-1=z\\ z^2+z-1=x \end{align}$$ My Try: if $x=y=z$ then the two triplets $(1,1,1)$ and ...
0
votes
0answers
46 views

Underdetermined system of equations

I am sorry in advance if the question I am going to ask is trivial. I have a problem of underdetermined system of equations (6 unknowns and three equations).All unknowns are between 0 and 1. Are there ...
0
votes
1answer
61 views

Solving system of two linear odes

I am trying to solve \begin{align} y_1'+B_{12}y_1=\beta_{12}y_2\\ Ay_2'+B_{21}y_2=\beta_{21}y_1, \end{align}with $y_1(0)=y_2(0)=y_0$. I find the eigenvalues to be ...
3
votes
1answer
317 views

Checking if a System of Polynomial Equations is Consistent

I'm trying to determine whether any solutions exist to a system of $(n+1)$ polynomial equations in $n$ unknowns. For example: $$ \begin{align*} xy&=-2\\ x^2-1&=0\\ y^3-3y^2+2y&=0 ...
0
votes
1answer
72 views

I am having problems with this system of equations [closed]

Hello guys im trying to work out the follow system with no success: $$\left\{\begin{array}{rcl}x+2y&=& 6 \\3x^2-xy+4y^2&=&48\end{array}\right. $$ why? thanks. I tried to solve it ...
1
vote
0answers
21 views

A nonlinear system of equation

In the real numbder set: $x,y,z$ are variable, $a_i,b_i,c_i,d_i$ is given ($i\in\{1,2,3\}$) What is the conditions for the following equations have solutions? $$a_1xy+b_1x+c_1y=d_1$$ ...
0
votes
0answers
17 views

bounds of solution to the system of nonlinear equations

I have a system of nonlinear equations: \begin{eqnarray*} F_1(x,y) &=& 0,\\ F_2(x,y) &=& 0, \end{eqnarray*} where $F_i(x,y)$ with $i=1,2$ are continuosly differentiable in $(x,y)$. ...
0
votes
0answers
29 views

2 Coupled variable-coefficient linear ODEs

I am trying to solve the following boundary-value problem for functions f(x) and g(x): $$ f'' + p_1\left[ f(1)-f(x) \right] + a(x) g - p_2(1-x) -p_6 = 0,\\ (c_1+c_2p_1)g'' - c_3 g^{(iv)} -a(x) f'' =0. ...
0
votes
1answer
36 views

Solve a system of equations.

I have a system of equations: \begin{align} & x_{21} (\frac{\partial}{\partial x_{11}}f_{1111})( x_{11} , x_{21}, y_{11} , y_{21} ) + \frac{y_{21}}{x_{11}^2} (\frac{\partial}{\partial ...
4
votes
3answers
79 views

Pair of PDEs to be solved together

I have the following pair of equations to be solved together to find the functions $H_{x}$ and $H_{y}$, which are the components of a vector $\bar{H}(x,y)=H_{x}(x,y)\hat{x}+H_{y}(x,y)\hat{y}$ in ...
1
vote
0answers
22 views

Solution of a DAE system of two ODE of second degree

I should solve the following DAE system: $$\ddot{x}(t)=-\alpha y(t)$$ $$\ddot{y}(t)=\beta x(t)$$ with the conditions: $x(t)\ge0$, $y(t)\ge0$ and $x(t)+y(t)=N$ with $N\gt 0$. I'm able to solve the ...
1
vote
2answers
53 views

For which values of $a, b$ does the system of equations NOT have any solutions?

I am trying to solve this math problem: For which values of $a$ and $b$ does the linear system represented by the augmented matrix not have any solution? $$ \left[ \begin{array}{ccc|c} ...
1
vote
1answer
35 views

Solving an augmented coefficient matrix so there are infinitely solutions

I am trying to figure out this math problem. For what values $a,b$ does the linear system have infinitely many solutions? This is the matrix $$ \left[ \begin{array}{ccc|c} ...
0
votes
1answer
16 views

system of equations with coefficients in finite field

Suppose we have three simultaneously equations with $4$ variables with coefficients in finite fields, i.e. $$\alpha_1A_1 + \beta_1B_1+\gamma_1C_1 + \theta_1D_1=x$$ $$\alpha_2A_1 + ...
3
votes
1answer
27 views

Find the polynomial function

Anybody knows how to find the polynomial function with evaluated values, where if the degree is $n$ I have $n+1$ values of the function like $f(0) = a_0, f(1) = a_1, \ldots, f(n) = a_n$.
0
votes
1answer
16 views

Help inverting a non-linear polynomial system of equations

I have a set of two equations like this $$ \gamma_3=\left(\frac{1}{\sqrt{1+2c_3^2+6c_4^2}}\right)^3 \left( \alpha_1\,c_3^3 + \alpha_2\,c_3c_4^2 + \alpha_3\,c_3c_4 + \alpha_4\,c_4\right)\\ ...
0
votes
3answers
29 views

Prove that $b^2 pr =q^2 ac$ using matrices

Let $i_1,i_2$ and $j_1,j_2$ be non-zero real roots of $ax^2+bx+c$ and $px^2+qx+r$ respectively, where a,p $\neq$0. If the system of equations $ i_1y+i_2z=0$ and $j_1y+j_2z=0$ has a non-trivial ...
2
votes
1answer
174 views

System of Linear Equations (3x6 matrix, parametric answer)

Solve the system \begin{array}{r@{}r@{}r@{}r@{}r@{}r@{}r@{}r} x_1 & - 2 x_2 & - 2 x_3 & & + 5 x_5 & - 4 x_6 & = & -1 \cr & & & - ...
0
votes
1answer
23 views

Cramer's rule and linear dependence/independence test

When you have the system of equations: $$ax + by = e\\cx + dy = f$$ And you do some row operations to eliminate $y$, we get: $$x = \frac{ed-bf}{ad-bc}\tag{1}$$ If we eliminate $x$ we get: $$y = ...
0
votes
0answers
30 views

Converting sums to matrix equations

I am able to transform basic sums to vector/matrix equations. But now I have something like: $$ c_{p,q} = \sum_{n=1}^N \sum_{r=1}^R \sum_{s=1}^S e_n x_{n-q-s,p} \cdot h_{r,s} \cdot g_r \cdot ...
1
vote
1answer
46 views

How can I write a system of equations puzzle if given the solutions? (work backwards?)

\begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix} How can I create a fun puzzle or word problem that would arrive at this solution above? For example, ...
11
votes
1answer
140 views

Cyclic system of equations

Consider the system of equations $$ \begin{align*} x^2+(1-y)^2&=a\\ y^2+(1-z)^2&=b\\ z^2+(1-x)^2&=c\\ \end{align*} $$ Compute $x(1-x)$ in terms of $a,b,c$. Edit: The question should say ...
3
votes
1answer
435 views

How to solve coupled linear 1st order PDE

It is fairly straight forward to solve linear 1st order PDEs by the method of characteristics. For example, if $\partial_tf+a\partial_xf=bf$ , we have that $\dfrac{df}{dt}=bf$ on the characteristic ...
0
votes
2answers
34 views

Solving coupled first-order linear ODEs

Basically this question comes from population modelling. Let y be the population of Lions and let x be the population of deer. By ignoring the effect of deer, we observe that $$dy/dt = k_2 y$$ ...
1
vote
1answer
31 views

Find the equation of the plane passing through $P(0,0,1)$ and containing $x=y=z$

Find the equation of the plane passing through $P(0,0,1)$ and containing $x=y=z$ a) y-z=0 b) x-z=0 c) z+x=1 d) x-y=0 My attempt: I considered the point $P(0,0,1)$ for hypothesis and ...
1
vote
0answers
43 views

Time needed to algebraically solve system of $15$ nonlinear equations with parameters

How long can I expect it will take to algebraically solve a system of $15$ nonlinear equations (without any numbers, only parameters), if I feed it into a computing software? I'm asking for symbolic ...
2
votes
2answers
73 views

How prove this equation have more one solution $x_{1}+x_{2}+\cdots+x_{n}=d,x_{1}x_{2}\cdots x_{n}=b$

Let $x_{i}\in \mathbb{Z},i=1,2,\ldots,n$, and such that $1\le x_{1}\le x_{2}\le\cdots\le x_{n}$. Show that $$\begin{cases} x_{1}+x_{2}+\cdots+x_{n}=d\\ x_{1}x_{2}\cdots x_{n}=b\\ b,d\in \mathbb{Z} ...
2
votes
2answers
66 views

How to determine the eigenvectors for this matrix

I have the matrix $$\left( \begin{array}{ccc} -\alpha & \beta \\ \beta/K & -\alpha/K \end{array} \right)$$ for which the eigenvalues are ...
2
votes
2answers
87 views

Solving a system of three linear equations with three unknowns

Is my working correct or am I completely wrong? Have I missed anything out? Any feedback is appreciated. Question: Consider the following system of equations $2x + 2y + z = 2$ $−x + 2y − z = −5$ ...
1
vote
1answer
67 views

a system of finite difference equations

Let $a,b>0$ such that $ab<1$ consider the system$$x_{t+1}=x_ty_t+ay_t$$ $$y_{t+1}=x_ty_t+bx_t$$ I would like you to help me answer the following: find values $a$ and $b$ ​​for which the ...