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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0
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1answer
62 views

solving equations by the method of elimination

$$\frac{a}{x}+\frac{b}{y}=\frac{a}{2}+\frac{b}{3} \;\;\; \ldots(i)$$ $$x+1=y \;\; \;\ldots(ii)$$ We have to solve for $x$ and $y$, only this time using the method of elimination. From equation ...
-1
votes
1answer
90 views

What are the steps required to solve this system of equations?

The system that I need to solve is $$ \begin{align} &i_1 + i_2+ i_3 &=0\\ &i_1+i_4+i_6 &=0\\ &i_5+i_6&=i_2\\ &-v_{s1} + i_1r_1 + i_3r_3 - i_4r_4 + v_{s4} &= 0\\ ...
0
votes
0answers
24 views

System of Modular Bivariate Polynomials

I have two bivariate polynomials in two unknowns: $x(y+a_{11}) + a_{12} \equiv b \pmod{m_1}$ $x(y+a_{21}) + a_{22} \equiv b \pmod{m_2}$ $x,y$ unknown All $a_{ij}$ terms and the constant $b$ are ...
1
vote
2answers
108 views

System of quadratic equations

How would you solve the following system of equations: $$ x^2 + y = 4 \\ x + y^2 = 10 $$ Thanks very much! I tried defining y in terms of x and then inserting in to the second equation: $$ y = 4 - ...
3
votes
1answer
46 views

system of matrix equations

I have the equation $ \mathbf{x}^T A \mathbf{x} = b $, where $b$ is a scalar, $\mathbf{x}$ a vector of size $M$, and A a matrix of size $M\times M$. $b$ and $\mathbf{x}$ are given. How many such ...
3
votes
2answers
115 views

Given ${x^2-x y+y^2 = 15, x y+x+y = 13}$ find the value of $x^2+6y$

Both x and y are real numbers and x > y . Given ${x^2-x y+y^2 = 15, x y+x+y = 13}$ find the value of $x^2+6y$ . I tried solving the second equation to get $y=(13-x)/(x+1)$ and substituted that in ...
2
votes
0answers
55 views

Crossing Orbits

I have a question here that I am stumped with. The path of an orbit of a planet around a distant sun is $2K^2 + 2I^2 = 50$. The planet orbits the sun at roughly $900$ million kilometers. The path of ...
2
votes
0answers
48 views

Problem reduced to analyzing solutions of a family of nonlinear systems of equations

This was posted on mathoverflow about two weeks ago and I got no response so I'm asking here in case anyone has any ideas. Original post is here. I was able to reduce a research problem relating to ...
4
votes
6answers
560 views

Find the value of $x$ and $y$ given this equation

So I have a College Admission test tomorrow and I am hoping that you could help me understand how to arrive at the solution to this: 1.) Given the following equations: $$3x-y=30\\ 5x-3y=10$$ ...
7
votes
2answers
210 views

How to solve this system for real $x,y,z$

Find the real values $x,y,z$ such that $$\begin{cases} x+y^2+z^3=21\qquad (1)\\ y+z^2+x^3=71\qquad (2)\\ z+x^2+y^3=45\qquad (3) \end{cases}$$ Thank you everyone. This problem have some nice methods, ...
4
votes
0answers
41 views

Solving a system of equations

I'm trying to prove the existence of a solution to the system of equations $$c_i = \gamma x_i + (1-\gamma) \frac{x_i^2}{\sum_{j=1}^\infty x_j}$$ for $i\in\{1,2,....\}$ where $\sum c_i=1$. I am also ...
1
vote
2answers
178 views

Solve a set of non linear Equations on Galois Field

I have the following set of equations: $$M_{1}=\frac{y_1-y_0}{x_1-x_0}$$ $$M_{2}=\frac{y_2-y_0}{x_2-x_0}$$ $M_1, M_2, x_1, y_1, x_2, y_2,$ are known and they are chosen from a $GF(2^m).$ I want to ...
1
vote
1answer
134 views

Using Lyapunov funtion, prove that a critical poin (0,0) is asymptotically stable.

Let a linear system $$ \ x'=-2x+x{y}^{2}\\ \ y'=-x^{3}-y\\ $$ Using Lyapunov funtion, prove that a critical point (0,0) is asymptotically stable.
4
votes
3answers
81 views

Is this solution correct?

$$\sqrt{x}+y=4\tag{A}$$ $$x+\sqrt{y}=6\tag{B}$$ Subtracting A from B, we have $$x-y -\sqrt{x}+\sqrt{y}=2$$ $$(\sqrt{x}-\sqrt{y})(\sqrt{x}+\sqrt{y}-1)=2$$ ...
0
votes
0answers
283 views

If $ a+b+c=4 ; a^2=b^2+c=6 ; a^3+b^3+c^3=8 $ Then find the value of $a^4+b^4+c^4$

If $a+b+c=4$ $ a^2=b^2+c=6$ (this is not symmetric equation) $a^3+b^3+c^3=8$ Then find the value of $a^4+b^4+c^4$
1
vote
3answers
43 views

system of differential linear equations $y'=\begin{pmatrix}1 & 1\\0 & 1\end{pmatrix}y$

find the solution to the problem $y'=\begin{pmatrix}1 & 1\\0 & 1\end{pmatrix}y, y(0)=\begin{pmatrix}4\\0\end{pmatrix}$ I know i have to find the eigenvalues and eigenvectors of the matrix ...
4
votes
3answers
225 views

Solving a system of equations, why aren't the solutions preserved?

I have the equations $$6x^2+8xy+4y^2=3$$ $\qquad$ $\qquad$ $\qquad$$\qquad$$\qquad$$\qquad$$\qquad$$\qquad$$\qquad$and $$2x^2+5xy+3y^2=2$$ This question can be found here, and the answer written by ...
2
votes
5answers
96 views

system of equations solving for positive $a,b,c$

i need help i need to find positive number $a,b,c$ solving this system of equations? $$(1-a)(1-b)(1-c)=abc$$ $$a+b+c=1$$ I found that $0<a,b,c<1$ and I try to solve it by try $(1-a)=a$, ...
5
votes
2answers
213 views

How to solve these three equations?

If α ,β ,γ are three numbers s.t.: $\ α^ \ $ + $\ β \ $ + $ γ \ $ = −2 $\ α^2 \ $ + $\ β^2 \ $ + $ γ^2 \ $ = 6 $\ α^3 \ $ + $\ β^3 \ $ + $ γ^3 \ $ = −5, then $\ α^4 \ $ + $\ β^4 \ $ + $ ...
0
votes
1answer
27 views

Can a bipartite summation graph have a unique solution?

Suppose we define a summation graph $G$ as follows: Each vertex $v \in G$ has a unique but unknown value ascribed to it. Each edge $e \in G$ is labelled with the sum of the values of the two vertices ...
3
votes
3answers
135 views

Did I solve this System of differential equations right?

My Problem is this given System of differential equations. $$y_{1}^{\prime}=5y_{1}+2y_{2} \\ y_{2}^{\prime}=-2y_{1}+y_{2}$$ I am looking for the solution. According to one of my earlier Questions, I ...
1
vote
3answers
52 views

Convert a line in $ \Bbb R^3 $ given as intersection of two planes to parametric form.

We have a line in $ \Bbb R^3 $ given as intersetion of two planes: $$ \left\{ \begin{aligned} A_1x+B_1y+C_1z + D_1 &=0 \\ A_2x+B_2y+C_2z + D_2 &=0 \\ \end{aligned} \right. $$ How to ...
1
vote
2answers
79 views

Solution of a non-linear system

What is the solution of the following system? $$ \begin{align} a \cdot e-b \cdot d & =\alpha \\ a \cdot f-c \cdot d & =\beta \\ b \cdot f-c \cdot e & =\gamma \end{align} $$ Where the ...
3
votes
1answer
110 views

Does this system have a root?

I have a set of nonlinear equations to solve which came up in my research. I take the conditional expected value of $N$ functions (which are $log()$) of $N$ independent non-identically distributed ...
2
votes
3answers
78 views

Set of ODE: how can I solve it?

I want to solve this system, but I have never solved a system of ODE, can you help me? $$ \begin{cases} \frac{dA}{dt}=-aA\\ \frac{dB}{dt}=aA-bB\\ \frac{dC}{dt}=bB \end{cases}$$ I have solved the ...
0
votes
1answer
80 views

Help with non-linear system of equations

This system of equations $$\begin{align} xy+yz+zx & =3 \\ \\ x^4+y^4+z^4 & =3\end{align}$$ How to solve this system of equations? Any help, Plz. Thank all
3
votes
3answers
161 views

Systems of Quadratic Equations Question

looking for help on this question. Solve the following systems of equations algebraically using the quadratic formula. $$\begin{align} y& =-x^2+2x+9\\ y& =-5x^2+10x+12\end{align}$$ Any help ...
0
votes
1answer
55 views

Is the solution stable

I've got the following system of equations: $x' = -x -2y + x^2y^2$ and $y'=x-\frac{1}{2} y - \frac{1}{2} x^3y$ I have to check whether zero solution (solution for x=y=0) is stable. Is it Lyapunov ...
0
votes
1answer
142 views

Visualise 3 simultaneous cubic equations

I have three equations of the form: $$\frac{i_1^3}{P_1}+i_1(Z_1+Z_2)+(i_2+i_3)Z_2-U_1=0$$ $$\frac{i_2^3}{P_2}+i_2(Z_1+Z_2)+(i_1+i_3)Z_2-U_2=0$$ $$\frac{i_3^3}{P_3}+i_3(Z_1+Z_2)+(i_1+i_2)Z_2-U_3=0$$ ...
0
votes
1answer
65 views

number of solutions in homogeneous system

What is the maximum possible number of solutions of homogeneous system $N \times N$ ($N$ variables, $N$ equations) of degree $2$, where in each equation we have linear terms in $x_i$ and quadratic ...
2
votes
2answers
683 views

Is there NO solution to this linear system of 3 equations, $3$ unknowns?

I have the following linear system: $$\begin{align} &x + y + 2z + 2 = 0 \\ &3x - y + 14z -6 = 0 \\ &x + 2y +5 = 0 \end{align}$$ I immediately noticed that there was no $z$ term in the ...
3
votes
2answers
415 views

The system of equations $x^2 + y^2 - x - 2y = 0$ and $x + 2y = c$

I have $(1.) \quad x^2 + y^2 - x - 2y = 0 \\ (2.) \quad x + 2y = c$ Solving for $y$ in $(2.)$ gives $y = (c - x) / 2$ Is there a way to simplify equation $(1.)$? Because at the end I arrive at ...
1
vote
2answers
86 views

Solving For Variables In Simultaneous Equations

I'm doing some work in linear algebra and these came up and I realized I don't know how to solve them as they have quadratics in them. I'm sure I've done this before but if someone could give me a ...
-2
votes
2answers
120 views

Help me with this this system of equations

Help me with this system of equations $$a+b = 3 -c$$ $$\frac{1}{a}+\frac{1}{b}= \frac{5}{12}-\frac{1}{c}$$ $$ a^3+b^3 = 45 -c^3$$
4
votes
3answers
204 views

How to solve this simultaneous equation of $3$ variables.

I've stuck in this equation system. No clue how to start ? $$\begin{eqnarray} x+y+z &=&a+b+c\tag{1} \\ ax+by+cz &=&a^{2}+b^{2}+c^{2}\tag{2} \\ ax^{2}+by^{2}+cz^{2} ...
3
votes
2answers
283 views

Solving 3 simultaneous cubic equations

I have three equations of the form: $$i_1^3L_1+i_1K+V_1+(i_2+i_3+C)Z_n=0$$ $$i_2^3L_2+i_2K+V_2+(i_1+i_3+C)Z_n=0$$ $$i_3^3L_3+i_3K+V_3+(i_1+i_2+C)Z_n=0$$ where $L_1,L_2,L_3,K,V_1,V_2,V_3,C$ and $Z_n$ ...
2
votes
1answer
57 views

How to frame this set of linear equations?

I have the following set of equations, as an example $2x + 1y + 2z = A$ $0x + 2y + 2z = A$ $1x + 2y + 1z = A$ I assume this can be rewritten as a matrix? How can I check if a solution exists such ...
3
votes
1answer
69 views

a system of equation

I want to show that the following system of equations does not have a solution, but I do not know how to do this $$w_1+w_2=\frac{1}{2}$$ $$w_1s_1+w_2s_2=\frac{1}{6}$$ $$w_1t_1+w_2t_2=\frac{1}{6}$$ ...
1
vote
3answers
111 views

Simultaneous solution(s) to $a^2+4b^2+4ab=0$ and $a^2+4b^2+32+16a-8b=0$?

Could you tell me just how should I solve this system: $$ a^2+4b^2+4ab=0\\ a^2+4b^2+32+16a-8b=0 $$ I can't remember the proceeding and it's driving me crazy. Thanks a lot
1
vote
2answers
167 views

How to prove the existence of solution of a non linear system of equations

Writing the ortogonality condition for any element of O(n), I've arrived to: If we take n=2, we know that $\Lambda\Lambda^{T}=\mathbb{I}$, so: $$\begin{pmatrix} x & y \\ z & t \end{pmatrix} ...
3
votes
2answers
131 views

How can I solve this system of non-linear equations?

I'm trying to solve this system of equations: $$\left\{ \begin{array}{lcr} a+c & = & 0\\ b+ac+d & = & 6\\ bc+ad & = & -5\\ bd & = & 6 \end{array} \right.$$ The book ...
3
votes
1answer
341 views

Consistent but apparently unsolvable system of equations

I have started learning linear algebra. One of the exercise problems is as below. Determine the value(s) of $h$ such that the matrix is the augmented matrix of a consistent linear system. $$ \left [ ...
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 ...
1
vote
2answers
237 views

Solve a system of time-independent ODE's with vector constants

I have to solve numerically this set of Ordinary Differential Equations $$ \frac{dx_1}{ds} = \frac{1}{x_1} \left[x_2 \left(a + \frac{x_2}{s}\right)-\alpha x_1 z\right]$$ $$ \frac{dx_2}{ds} = ...
-4
votes
2answers
186 views

Solve the system of equations:

Solve the system of equations: $$\begin{matrix} 2\sqrt[4]{\frac{x^4}{3}+4}=1+\sqrt{\frac{3}{2}.y^2} \\ 2\sqrt[4]{\frac{y^4}{3}+4} = 1+\sqrt{\frac{3}{2}.x^2} \end{matrix}.$$
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
2answers
113 views

Existence of invariant set in dynamical system generated by ODE

Is there any nonempty, compact and invariant set in dynamical system generated by this system of equations? $x'=x+\sin{(xy+2)}-7$ $y'=-y+\arctan{(x^2+y^3-6)}$ My idea is to use this fact: Not ...
1
vote
3answers
116 views

Solving a linear system of equations

$$\begin{cases} 3x - 2y + z = 8 \\ 4x - y + 3z = -1\\ 5x + y + 2z = -1 \end{cases}$$ Form two equations with y elimanted. It would be really helpful too see what you guys wrote.
7
votes
6answers
355 views

Solve $5a^2 - 4ab - b^2 + 9 = 0$, $ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0$

Solve $\left\{\begin{matrix} 5a^2 - 4ab - b^2 + 9 = 0\\ - 21a^2 - 10ab + 40a - b^2 + 8b - 12 = 0. \end{matrix}\right.$ I know that we can use quadratic equation twice, but then we'll get some ...