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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1answer
86 views

How can I solve this equations? [closed]

Here is a system of equations: $$\left\{ \begin{eqnarray} x^2+2y^2-2yz=100 \\ 2xy-z^2=100 \end{eqnarray} \right. $$ What's the value of $x$ and $y$? According to my math teacher it's a very hard ...
2
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4answers
67 views

How to solve this kind of equation $(x^y=y^x)$

I'm little bit stuck with this system of equations : $x^y=y^x$ and $x^3=y^2$ An obvious solution is $(x,y) = (1,1)$ but what about the solution $(9/4,27/8)$ ? I know the relation $a^r=e^{r ...
1
vote
1answer
37 views

Solution of $d^2u/dx^2 + u/A = 0 \ (\text{or } \ C),$ with conditions

Does the following ODE: $$d^2u/dx^2 + u/A = 0 \quad (\text{or } \ C),$$ have a solution with the conditions: $$ \left.\frac{d^2u}{dx^2}\right|_{x=0} = 0, $$ $$u(x=0) = B$$ and $$ ...
2
votes
0answers
21 views

Find a reduced echelon basis from a reduced echelon matrix.

The reduced row matrix was this ---> $\begin{pmatrix}1&2&0&1&0\\0&0&1&3&0\\0&0&0&0&1\\0&0&0&0&0&\end{pmatrix} = 0$ So i computed ...
1
vote
1answer
22 views

Unique solution to a arbitrary non-linear system under monotonicity assumptions

I have a map $f:\mathbb{R}^n\times\mathbb{R}^m \to \mathbb{R}^n$ of two arguments $x, y$, which has a following properties: The jacobian matrix of $f$ wrt to the first argument $\frac{\partial ...
1
vote
4answers
139 views

Solutions for the given system with fractions

I have to solve in $\Bbb{R}$ the following system : $$ \ \left\{ \begin{array}{ll} \frac{y}{x}+\frac{x}{y}=\frac{17}{4} \\ x^2-y^2=25 \end{array} \right.$$ For this one I am ...
0
votes
0answers
17 views

A system of absolute value equalities

Background: I'm trying to show that the transformation $T:\Bbb R^n\to\Bbb R^n$ defined by $T(x_1,\dots,x_n) := (|x_2-x_1|,|x_3-x_2|,\dots,|x_1-x_n|)$ is (or is not, this is out of curiosity only) ...
3
votes
2answers
37 views

If Sue buys A, she will have $\$1.50$ left; if she buys B, she will have $\$2$ left. Given that 2A=3B, how much money does she have?

Problem statement I can see the answer is B, but only using elimination. Surely I should be able to convert the question to an equation, e.g. 2F = 3L... to make it simpler.
0
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1answer
22 views

How many of each type of player should you order to minimize your cost?

Your electronics store sells two types of portable CD players. The first type, A, costs 70 dollars and you make a 25 dollar profit on each one. The second type, B, costs 60 dollars and you make a 20 ...
2
votes
1answer
23 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 ...
0
votes
1answer
70 views

Solving the system with logarithms

I tried solving the system $ \begin{cases} (4x)^{\log_2 (2y)} = 64 \\ (8y)^{\log_2 (2y)} = 256 \end{cases} $ several times but still keep getting wrong solutions.
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3answers
46 views

Solving a system of three equations: $d = s\cdot 3, c = s\cdot 1.5, c = 2\cdot d$.

Sorry if this is not the right place for this sort of question, but I am at a lost. My niece has some summer homework, and neither of us have a clue how to solve this question. Its been too long since ...
0
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0answers
46 views

How to solve a system of first-order partial differential equations?

I have a system of first-order partial differential equations. \begin{align} & -\frac{a}{a_1} \frac{\partial P_{12}}{\partial a} - \frac{a b}{a_1 b_1} \frac{\partial P_{12}}{\partial b} + ...
0
votes
3answers
139 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 - ...
2
votes
3answers
44 views

Finding the perimeter of the room

If the length and breadth of a room are increased by $1$ $m$, the area is increased by $21$ $m^2$. If the length is increased by $1$ $m$ and breadth is decreased by $1$ $m$ the area is decreased by ...
0
votes
3answers
23 views

Finding the angles of a parallelogram.

In a parallelogram, one angle is $2/5th$ of the adjacent angles. Determine the angles of the parallelogram. I tried the following, Let the adjacent angles be $2x$ Let the other angle be $y$ ...
0
votes
2answers
32 views

The perimeter of a rectangle is 48 meters and its area is 135 m^2. Determine the sides of the rectangle.

The perimeter of a rectangle is 48 $m$ and its area is $135$ $m^2$. Determine the sides of the rectangle. I tried the following, Perimeter$=$$48$ $m$ Let the length be $x$ m and the breadth be $y$ m ...
4
votes
2answers
68 views

Mr. and Mrs. Ahuja weigh x and y kg. Find their present weights.

Mr. and Mrs. Ahuja weigh $x$ kg and $y$ kg respectively. They both take a dieting course at the end of which Mr. Ahuja loses $5$ kg and weighs as much as the wife weighed before the course. Mrs. Ahuja ...
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1answer
54 views

Solving Systems of Equations..!! [closed]

I actually don't want to solve the systems of equations. I just want to let them equal each other so I can cancel one of them and solve the other one. Example: $E_1\quad x-y=0$ $E_2\quad 2x-2y=0$ ...
0
votes
1answer
41 views

The denominator of a fraction is 4 more than twice the numerator. Determine the fraction.

The denominator of a fraction is $4$ more than twice the numerator. When both the numerator and denominator are decreased by $6$, the denominator becomes $12$ times the numerator. Determine the ...
1
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0answers
32 views

System of quadratic equations for a tetrahedron

I know the dimensions of the base of a tetrahedron and the angles between the non base sides at the apex. I want to know the lengths of the three non base sides. Let the base's corner points be $A, ...
0
votes
1answer
13 views

Solution of a matrix equation with a triangular matrix

Given the matrix: $$B = \begin{bmatrix} b_1 & 0 & 0& ... \\[0.3em] b_2 & b_1 &0 & ... \\[0.3em] b_3 & b_2 & b_1 \\... ...
2
votes
0answers
57 views

Eliminate variable in trigonometry equations

Say you have the equations: \begin{align} -S_1\sin\left(2\psi+\theta\right)+S_2\cos\left(\psi\right)&=S_3\\ S_1\cos\left(2\psi+\theta\right)+S_2\sin\left(\psi\right)&=S_4 \end{align} or ...
1
vote
1answer
43 views

A farmer sold a calf and a cow for Rs 760. Find the cost of each.

A farmer sold a calf and a cow for Rs. 760 Thereby making a profit of 25% on the calf and 10% on the cow. By selling them for Rs. 767.5 he would have raised a profit of 10% on the calf and 25% on ...
0
votes
1answer
19 views

Knowing the total price of stamps of two denomination, find the number of stamps of each kind

A man buys postage stamps of denominations $3$ paise and $5$ paise, for Rs $1$. He buys $22$ stamps in all. Find the number of $3$ paise stamps bought by him. (100p= 1 Rs) I tried, Let the number of ...
0
votes
2answers
54 views

How to find the intersection points of lines that are normal to two curves?

Let I have two curves, \begin{gather} f(x)=\frac{x^3}{4}+1 \\ g(x)=\frac{(x-\tfrac{1}{2})^3}{7}+\tfrac{1}{2} \end{gather} There are zero or more lines that are normal to both curves. In other words, ...
1
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0answers
59 views

Long-time asymptotic behaviour of a system of two ODEs

We have the following nonlinear ODE: $$ f' = af-bg -(f+g)^k \bigl(f'(0) +g'(0)\bigr) + f'(0), $$ $$ \bigl(G-T(x)\bigr) g' = -af+bg - g'(0), $$ where $a,b,k,G$ are constants, $f'(0)$ and $g'(0)$ are ...
1
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0answers
47 views

intersection of a line and plane on a 3-sphere

Suppose I have two 4D points, $\mathbf{a}=(a_1,a_2,a_3,a_4)$ and $\mathbf{b}=(b_1,b_2,b_3,b_4)$, that both lie on a unit 3-sphere (i.e. unit distance from origin). In addition, I have a 2-D plane that ...
2
votes
0answers
50 views

Solving a system of equation and finding the largest possible value of one of the variables

This problem comes from question 5 in the PUMAC Algebra A competition (link here): Suppose $w, x, y, z$ satisfy $$w+x+y+z=25$$ $$wx+wy+wz+xy+xz+yz=2y+2x+193$$ The largest possible value of $w$ can ...
0
votes
3answers
38 views

number of ordered pairs of integers (x,y) satisfying the equation

i need to find number of ordered pairs of integers(x,y) satisfying below equation. $$x^2 + 6x + y^2 = 4$$ i have tried and i think x<0 . is there a specific way to solve such equations?
2
votes
0answers
31 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} = ...
1
vote
3answers
30 views

number of solution to the given equation.

a,b,c, are all non-negative integers such that a + b + c=100 and 1000a + 300b + 50c = 10000 How many such triplets are possible? i have tried to reduce ...
0
votes
0answers
40 views

Strategies to work with system of trigonometric inequality

I'm trying solve this problem using matlab, anybody know good strategies to work with system of trigonometric inequalities such as $ ...
2
votes
1answer
82 views

Asymptotic expansion on 3 nonlinear ordinary differential equations

The 3 nonlinear differential equations are as follows \begin{equation} \epsilon \frac{dc}{dt}=\alpha I + \ c (-K_F - K_D-K_N s-K_P(1-q)), \nonumber \end{equation} \begin{equation} \frac{ds}{dt}= ...
1
vote
1answer
34 views

solving system of equations(nonlinear)

I am trying to solve the following system of equations: $$\frac{kq^2}{d}=mg(L-L\cos(t))+\frac{kq^2}{r}$$ $$\sin(t)=\frac{x}{L}$$ $$r^2=(L-L\cos(t))^2+(x+d)^2$$ The parameters are: $k,L,d,q,m,g$ The ...
2
votes
1answer
25 views

Can I convert between a rotation about an axis and a rotation according to two angles (all in 3D) without solving a system of nonlinear equations?

I am writing a program that needs to be able to switch between a rotation described by 2 angles to a rotation described an axis and one angle. I found one way to do this from this question, which ...
2
votes
3answers
79 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 ...
0
votes
1answer
75 views

Solving for Center Manifold with Parameter

I have a system of ODEs given by $$\frac{dX}{d\tau}=\beta X\left(1 - \frac{X+Y}{N}\right)$$ $$\frac{dY}{d\tau}= Y\left(1 - \frac{X+Y}{N}\right)$$ where $\beta $ is a parameter. How should I ...
2
votes
0answers
81 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
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1answer
71 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
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0answers
34 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 - ...
2
votes
3answers
62 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
1answer
43 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 ...
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
15 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
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0answers
47 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 ...
0
votes
4answers
62 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 $|x+y|= 6$??
2
votes
3answers
410 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 ...
3
votes
1answer
88 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
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0answers
22 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 ...