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
votes
3answers
424 views

Solution of 3 equations in 3 unknowns [closed]

Find the value of $c$ which makes it possible to solve: $$u+v+2w=2,$$ $$2u+3v-w=5,$$ $$3u+4v+w=c$$
3
votes
4answers
1k views

Steps to solve this system of equations: $\sqrt{x}+y=7$, $\sqrt{y}+x=11$

I want to solve this system of equations, I have been out of Maths for a long!! $$\sqrt{x}+y=7$$ $$\sqrt{y}+x=11$$ Just wondering easiest step to find values for $x$ and $y$ from the above ...
0
votes
8answers
189 views

Systems of linear equations to calculate $\alpha$ and $\beta$

Point $1$: When there is $1$ car passing the road, the average speed is $50$ km/h. Point $2$: When there are $5$ cars passing the road, the average speed is $45$ km/h. Point $3$: When there are $12$ ...
6
votes
3answers
680 views

Three-variable system of simultaneous equations

$x + y + z = 4$ $x^2 + y^2 + z^2 = 4$ $x^3 + y^3 + z^3 = 4$ Any ideas on how to solve for $(x,y,z)$ satisfying the three simultaneous equations, provided there can be both real and complex ...
-2
votes
0answers
58 views

Writing systems of linear equations and matlab help appreciated [duplicate]

Does anyone know how I would go about answering the following question? A traffic engineering company has installed some trac cameras along a one lane road to find a relation between the number of ...
20
votes
5answers
646 views

Solving a peculiar system of equations

I have the following system of equations where the $m$'s are known but $a, b, c, x, y, z$ are unknown. How does one go about solving this system? All the usual linear algebra tricks I know don't apply ...
8
votes
5answers
274 views

Given $x+y$ and $x\cdot y$, what is $x^3+ y^3$ ?

I have been looking at an assortment of high school number sense tests and I noticed a reoccurring problem that states what x+y is and what $x\cdot y$ is then asks for $x^3+ y^3$. I want to know how ...
4
votes
4answers
496 views

What is the non-trivial, general solution of these equal ratios? [closed]

Provide non-trivial solution of the following: $$\frac{a}{b+c}=\frac{b}{c+a}=\frac{c}{a+b}$$ $a=?, b=?, c=?$ The solution should be general.
4
votes
2answers
121 views

A calculus problem with functions such that $f''(x) = g(x)$ and $g''(x) = f(x)$

Let: $f(x)$ and $g(x)$ be twice differentiable, non-decreasing functions. $f''(x) = g(x)$ and $g''(x) = f(x)$. $f(x) \cdot g(x)$ is a linear function. Then we have to show that $f(x) = g(x) = ...
3
votes
1answer
47 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 ...
2
votes
5answers
76 views

Why a linear numerator for fractions with irreducible denominators?

For example: (2x^3+5x+1)/((x^2+4)(x^2+x+2)) breaks down to (ax+b/(x^2+4))+(cx+d/(x^2+x+2)). I have been told that since the denominators are irreducible, the numerators will be either linear or ...
2
votes
1answer
60 views

Eigenvectors Trajectories

I got stuck with a problem while studying for a control systems exam. It goes as following: "Look at the picture of trajectories of a linear, time-invariant system with the form: ...
1
vote
4answers
92 views

Reducing the System of linear equations

\begin{align*} x+2y-3z&=4 \\ 3x-y+5z&=2 \\ 4x+y+(k^2-14)z&=k+2 \end{align*} I started doing the matrix of the system: $$ \begin{pmatrix} 1 & 2 & -3 & 4 \\ 3 & -1 & 5 ...
0
votes
3answers
135 views

Solving a system of nonlinear (quadratic) equations

Consider the following system of equations: $$\begin{align} (x + 1)^2 [(p - l)^2 + (q - m)^2] &= (a - l)^2 + (b - m)^2 \\ (x + 1)^2 [(p - a)^2 + (q - b)^2] &= x^2[(a - l)^2 + (b - ...
0
votes
1answer
75 views

Linear systems. Please help me solve this

Please help me solve this. Consider for every real number $a$ the linear system of equations: $$ \begin{align} x +( a + 1 )y + a^2 z &= a^3 \\ (1-a)x +( 1 - 2a )y &= a^3 \\ x +( a ...
-1
votes
2answers
39 views

Proof of axis of symmetry equation [closed]

Because quadratic functions are symmetrical how do you prove the axis of symmetry equation. $x=(-b/(2a))$
-2
votes
0answers
46 views

Writing systems of linear equations [duplicate]

Would anyone be able to help me with the following question? Thank you. Point 1: When there is 1 car passing the road, the average speed is 50km/h. Point 2: When there are 5 cars passing the road, ...
13
votes
4answers
755 views

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 ...
5
votes
1answer
199 views

Complex numbers system of equations problem with 5 variables

Let $z_0$,$z_1$,$z_2$,$z_3$ and $z_4$ such that $z_i\in C$ that hold: $$(1)|z_0|=|z_1|=|z_2|=|z_3|=|z_4|=1$$ $$(2)z_0+z_1+z_2+z_3+z_4=0$$ $$(3) z_0z_1+ z_1z_2+z_2z_3+z_3z_4+z_4z_0=0$$ Prove that ...
5
votes
2answers
1k views

System of equations: $x^2+y=7, y^2+x=11$ [duplicate]

Possible Duplicate: Steps to solve this system of equations During the flight from Moscow to Yerevan my neighbor gave me the following problem: Solve the system: ...
5
votes
5answers
746 views

Solving a set of recurrence relations

I have the 7 following reccurence relations: $A_n = B_{n-1} + C_{n-1}$ $B_n = A_n + C_{n-1}$ $C_n = B_n + C_{n-1}$ $D_n = E_{n-1} + G_{n-1}$ $E_n = D_n + F_{n-1}$ $F_n = G_n + C_n$ $G_n = E_n + ...
3
votes
2answers
63 views

Finding the general solution to a system of differential equations

How can I solve the following system of differential equations? I am getting confused with the constants of integration... $$\dot{x}=2x-(2+y)e^{y}$$ $$\dot{y}=-y$$ I know that $y=Ce^{-t}$ and the ...
2
votes
0answers
79 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
2answers
54 views

Describe all integers a for which the following system of congruences (with one unknown x) has integer solutions:

$$x\equiv a \pmod {100}$$ $$x\equiv a^2 \pmod {35}$$ $$x\equiv 3a-2 \pmod {49}$$ I'm trying to solve this system of congruences, but I'm only familiar with a method for solving when the mods are ...
2
votes
1answer
1k views

Polar coordinates differential equation

I have the following ODE: $$\dot x=-y(x^2+y^2), \dot y=x(x^2+y^2)$$ I want to sketch the phase portrait (manually) and I want to find the flow $\phi_t$, the orbit $O(x_0)$ and the limit set ...
1
vote
1answer
34 views

Finite differences coefficients

I'm interested in deriving a forward finite difference approximation for the gradient of a function, $f(x)$, at the point $x = x_i$ using $k+1$ points. If the spatial domain is uniformly discretized, ...
1
vote
1answer
83 views

Roots of unity and a system of equations by Ramanujan

Is it immediately apparent that the solution to the system of equations, $$\begin{aligned} x_1^2 &= x_2+2\\ x_2^2 &= x_3+2\\ x_3^2 &= x_4+2\\ &\vdots\\ x_n^2 &= x_1+2\\ ...
1
vote
3answers
111 views

Solving the system $(18xy^2+x^3, 27x^2y+54y^3)=(12, 38)$

While answering this question, I got myself stumped with this crazy system with an evil graph: $$\begin{cases} 18xy^2+x^3=12 \\ 27x^2y+54y^3=38 \end{cases}$$ and I wonder whether there is some slick ...
4
votes
2answers
176 views

Solving system of multivariable 2nd-degree polynomials

How would you go about solving a problem such as: \begin{matrix} { x }^{ 2 }+3xy-9=0 \quad(1)\\ 2{ y }^{ 2 }-4xy+5=0 \quad(2) \end{matrix} where $(x,y)\in\mathbb{C}^{2}$. More generally, how would ...
3
votes
2answers
291 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
22 views

Find the minimum value of C subject to the given constraints.

C=2x+5y Constraints: x+y>=2 2x-3y<=-6 3x-2y>=6 A-42 B-4 C-49 D-10 I encountered this question while doing the Systems of Linear Equations and Inequalities test at ...
2
votes
0answers
30 views

What is the solution to the system $\frac{df_n}{dt} = kf_{n-1}-(k+l)f_n+lf_{n+1}$?

I'm trying to solve the system $$ \begin{matrix} & \frac{df_1}{dt} = kf_1+lf_2 \\ & \vdots \\ & \frac{df_n}{dt} = kf_{n-1}-(k+l)f_n+lf_{n+1} \\ & \vdots \\ & \frac{df_N}{dt} = ...
2
votes
1answer
72 views

Method of characteristics for a system of pdes

I can do parts a) and b) as follows $\begin{pmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1\end{pmatrix}\frac{\partial}{\partial{}x}\begin{pmatrix} u \\ v \\ w\end{pmatrix}+\begin{pmatrix} ...
2
votes
1answer
73 views

Can all equation systems be reduced to the identity matrix?

I'm trying to learn about solving equation systems using the Gauss-Jordan method. So, you have to convert the equation system to a matrix, and then reduce it to the identity. When you transform it to ...
2
votes
2answers
578 views

system of equations $\sqrt{x}+y = 11$ and $x+\sqrt{y} = 7$. [duplicate]

If $x,y\in \mathbb{R}$ and $\sqrt{x}+y = 11\;$ and $x+\sqrt{y} = 7$. Then $(x,y) = $ $\underline{\bf{My\;\; Try::}}$ Let $x=a^2$ and $y=b^2$, Then equation is $a+b^2 = 11$ and $a^2+b = 7$. ...
1
vote
2answers
73 views

System of Nonhomogeneous DEs - Help Solving???

I'm studying for finals at the moment and could use some help with solving the particular solution for this system of nonhomogeneous differential equations: $x' = \begin{bmatrix}1 & 0\\ 2 & ...
1
vote
3answers
66 views

Partial fraction decomposition of a complicated rational function

Find the partial fraction decomposition of the rational function $\displaystyle \frac{2x^3+7x+5}{(x^2+x+2)(x^2+1)}$ I have tried dividing first but keep running into problem after problem, please ...
1
vote
3answers
1k views

For what values of $k$ does this system of equations have a unique solution?

Here's my system of equations: $\begin{cases}y + 2kz = 0\\x + 2y + 6z = 2\\kx + 2z = 1\\ \end{cases}$ So I have ...
0
votes
2answers
30 views

Classify critical point of linear system

For this linear system: $\dfrac{dx}{dt}=x+y-2$ $\dfrac{dy}{dt}=x-y-4$ I've found the critical point to be $(1,1)$ but now I want to classify it. How do I do it?
0
votes
1answer
39 views

Solve a system of inequalities

$$\begin{cases} \log_{2}^{2}(-\log_{2}x) + \log_{2}\log_{2}^{2}x \leq 3 & \\-4 |x^2-1|-3\geq \frac{1}{x^2-1}& \end{cases}$$ What I've tried: Make substitution $t=x^2-1$ and solve second ...
0
votes
1answer
83 views

Solving a nonlinear system of differential equations in MATLAB or Mathematica

Is it possible to solve the system $$\dot{W}=A\left(k-\frac{M}{W}\right)$$ $$\dot{M}=B\left(k-\frac{M}{W}\right)$$ with initial conditions $$W(0)=w_0$$ $$M(0)=m_0$$ in MATLAB or Mathematica? If so, ...
0
votes
2answers
108 views

System of Linear Equations with dependence on $a$

I gotta solve this System of linear equations dependent on $a$: $$x+y+z=1$$ $$-2x+2y+az=3$$ $$-ax+y+2z=2$$ I'm transforming this to a matrix. $$ M_1 = \left[\begin{array}{ccc|c} 1 & 1 & 1 ...
0
votes
1answer
143 views

Visualise 3 simultaneous cubic equations

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