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
69 views

Is there any simple analytic method for solving $\sqrt{x}+y=7$ and $x+\sqrt{y}=11$ simultaneously. [duplicate]

I am thinking of a nice and simple analytic method to solve the following equations simultaneously: $$\sqrt x+y=7;\\x+\sqrt y=11.$$ To my suprise I can't. But, I solve the system numerically using ...
0
votes
2answers
27 views

Initial value problem with a delta term

Im having trouble solving this initial value problem. I know how to solve it without the delta-term (C1*e^(lambda*t)*S1 + C2*e^(lambda*t)*S2), but how do i solve it with a delta term?
0
votes
2answers
51 views

Substitution vs Elimination in Solving Systems of Equations

When solving systems of equations, is it more efficient in terms of time to solve it using substitution or elimination, and what are your reasons for saying so?
12
votes
2answers
653 views

System of non-linear equations.

I have to find all triplets $(x,y,z)$ that satisfy: $$x^{2012} + y^{2012} + z^{2012} = 3\\x^{2013} + y^{2013} + z^{2013} = 3\\x^{2014} + y^{2014} + z^{2014} = 3$$ I've found the trivial solution ...
0
votes
0answers
20 views

Problem of choice under conditions of certainty and with immediate effect.

A transport company expects to deliver 8,000 tons of goods per month for six months, 6000 tons per month for three months, 5000 tons in July, 5000 tons in August, and 4000 tons in January. Each truck ...
3
votes
2answers
81 views

Find all complex number $z\in\Bbb{C}$ such that $\vert z\vert=\vert z^{-1}\vert=\vert z-1\vert$

Find all complex number $z\in\Bbb{C}$ such that $$\vert z\vert=\vert z^{-1}\vert=\vert z-1\vert$$ I tried to write $z=a+ib$, clearly $z=1$ is not a solution. I have to solve $$\left\{ ...
0
votes
1answer
28 views

Transformation of inverse to a system of linear equations

I have $X = (U'WU)^{-1}U'$ to be solved. Suppose $U'$ is $3 \times 7, W$ is $7 \times 7$ positive definite matrix, $U'$ is of rank 3. So, I transformed $(U'WU)^{-1}U'$ as $(U'WU)^{-1}U'WU = I\\ XWU ...
0
votes
3answers
45 views

Is there anyway to find the values for equation with two variables

Is there mathematical anyway to find the values for equation with two variables? as example: I have y = (20x+3)r+x and y is 50. then what is x and r values?
0
votes
2answers
51 views

How can I find the R values

I have the following equations : $$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N= R - S \end{cases}$$ - And I have the $B$ values, e.g : 834343, 3253538, ...
3
votes
2answers
56 views

Can a straight line be drawn from origin to co-ordinate X,Y?

Given a co-ordinate P(X,Y), can a straight line be drawn from origin to P, if there is wall existing with end points A(X1,Y1) and B(X2,Y2)? My Approach: I first of all wrote the equations from origin ...
0
votes
1answer
60 views

how can I find equation variables?

I have the following equations : $$\begin{cases}K = \frac{B – 3}{20}\\ K = (20S+3)R+S\\ K = 20S^2 + (20N+7)S + N\\ N=S-R \end{cases}$$ - And I have the $B$ values, e.g : 173, 283, 2343, 834343 ...
4
votes
4answers
512 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.
0
votes
0answers
12 views

unknown function: calculation of coefficients in series expansion up to a given degree

I am trying to solve an functional equation of unknown $h\mapsto h(x)$ ($x\in\mathbb{R}$, in the neighbourhood of $0$): $$\mathcal{F}(h)=\mathcal{G}(h) \qquad (*)$$ (assume $\mathcal{F}$ and ...
1
vote
0answers
19 views

Verification - Matrices and Linear Equations Part 1

Would just like to verify my Answers and bounce off my ideas and thinking with someone as I feel quite alone in this course. I am usually great at maths and enjoy it but these matrices and linear ...
1
vote
1answer
36 views

Solution to two equations with three unknowns

So I'm a student studying through correspondence and I need some help. This is an assignment question, and I have tried everything I know how, to answer it which has lead me to the conclusion that ...
1
vote
2answers
235 views

Matrix Equation- solution

Sir, We have given $A= \begin{bmatrix}q_1 & q_2&q_3 \\ q_4 & q_5&q_6\\ q_7 & q_8&q_9 \end{bmatrix} \tag 1$. A is a matrix with determinant 1,orthogonal , invertible and ...
0
votes
4answers
65 views

How to solve these simultaneous equations using any better way?

This problem is easy, but I am just curious whether there is any better and more elegant method of solving. Solve the simultaneous equations: $$2x^2+5xy+2y^2=0,$$ $$x^2-y^2=1.$$ The way I solve it ...
0
votes
1answer
67 views

Finding the fixed points of a recurrence relation (and systems of) analytically?

How would I go about finding the fixed points of the following recurrence? $$X_n = 2X_{n-1}(2- 3X_{n-1}) + X_{n-1}$$ And therein, determining their stability analytically? Also, how does one find ...
3
votes
2answers
42 views

Solving $4y^4 - 4x^4 + x + y = 0$ (equation system of partial derivates)

I need help solving the following equation system: $$ \frac{\partial}{\partial x} = 8xy + 4y^2 + \frac{y}{x^2 + y^2} = 0 $$ $$ \frac{\partial}{\partial y} = 8xy + 4x^2 - \frac{x}{x^2 + y^2} = 0 $$ ...
2
votes
0answers
36 views

Method of characteristics for systems of PDE (vs. Lewy's example)

Main question: How does the method of characteristics generalize for systems of first order PDE, as opposed to scalar PDE? Namely, is there such a generalization at all, and if so what information ...
0
votes
1answer
47 views

How to solve a nonlinear system of three equations involving rational functions?

How do I get $a$, $b$, and $c$? Given $$X=\frac{a+\frac{1}2b}{a+b+c}$$ $$Y=\frac{b(\frac{\sqrt3}{2})}{a+b+c}$$ $$Z=\frac{76a+150b+29c}{255}$$ in other words How do i get $a$, $b$, and $c$ on the ...
0
votes
2answers
46 views

How to solve the system $ax>y+z$, $by>x+z$, $cz>x+y$ in positive numbers?

Let $a>b>c>1$. How to find solutions in positive numbers of the following system? \begin{cases} ax>y+z \\ by>x+z \\ cz>x+y \end{cases}
0
votes
1answer
25 views

How to find parameters that minimize the sum of squares, using Matlab?

I have a system of linear equations in the following form. How can I solve it in Matlab? $$\operatorname*{argmin}_{a,b} \sum_{i,j} [X(i,j)-a\times Y(i,j)-b]^2$$ Where X and Y are known. I need to ...
3
votes
0answers
60 views

Analytic solution for system of Digamma function equations

Peace be upon you, There is a while, I am seeking for the analytic solution of $\alpha$ and $\beta$ in this system \begin{align*} \begin{cases} \psi(\alpha)-\psi(\alpha+\beta)=c_1\\ ...
4
votes
2answers
134 views

How can I solve this system of equations?

Here is a system of equations: $$\begin{cases} x^2 + 10y = 41\\ y^2-2z = 23\\ z^2-6x = 17 \end{cases} $$ What's the value of $x$ and $y$ and $z$?
0
votes
1answer
92 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
votes
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
42 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
22 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
23 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
143 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
19 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) ...
2
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
votes
1answer
23 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
24 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.
1
vote
3answers
48 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
votes
0answers
47 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
143 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
51 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
43 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
74 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 ...
-1
votes
1answer
55 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
60 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
vote
0answers
34 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
14 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
60 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
46 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
20 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 ...