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
41 views

Trouble Solving a system of 3 equations

I'm having trouble solving a system of 3 equations. The set of equations in question is shown below $C_a=\frac{R_a}{\frac{R_a}{r_a}+\frac{R_b}{r_b}+\frac{R_c}{r_c}}, \quad ...
0
votes
2answers
35 views

How do I solve a linear system with two variables and three equations?

To be specific here is the system: $$x-2y=0 \tag{1}$$ $$x-2(k+2)y=0 \tag{2}$$ $$x-(k+3)y=-k \tag{3}$$ I have already solved it for equations $(1)$ and $(2)$... what should I do with the 3rd ...
2
votes
1answer
14 views

Commutative Monoid - matrix set

Let $M$={$\begin{bmatrix} a & b & c \\ c & a & b \\ b & c & a \end{bmatrix}|a,b,c\in \mathbb{R}, a+b+c=0$}. The matrices in $M$ are a special kind of Toeplitz matrices ...
2
votes
4answers
140 views

Do row operations change the column space of a matrix?

I know that (i) row operations do not change the row space (ii) column operations do not change the column space and (iii) row rank = column rank (but this is sort of unrelated, I think). But, ...
0
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0answers
26 views

system of equations using the Elimination Method

Solve the system of equations using the Elimination Method. 3x-4y+0z=63 -2x-1y+0z=-9 5x-3y+0z=72 (x,y,z)=( , , ) I have tried this a couple of times and ...
1
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0answers
23 views

Systems of equations word problem

A goldsmith has two alloys, the first containing $77\%$ and the second containing $96\%$. If $x$ grams of the first alloy are mixed with $y$ grams of the second, obtaining $100$ grams of an alloy ...
8
votes
1answer
103 views

Evaluate $a^2+b^2+c^2$

I found this questions from past year maths competition in my country, I've tried any possible way to find it, but it is just way too hard. If $a, b, c$ are distinct numbers such that $a^2 - bc = ...
0
votes
2answers
49 views

Elementary Substitution in Solving Equations - Why it works

To solve a system of linear and certain non-linear equations, the substitution method is widely used by elementary and high school students. As explained here, to solve this simple system of linear ...
0
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0answers
54 views

System of equations to solve this nested radical.

The nested radical $$1.75793\approx\sqrt{1+\sqrt{2+\sqrt{3+\cdots}}}$$ has yet to be given a closed form. However, nested radicals of the form, $$\sqrt{A+B\sqrt{A+B\sqrt{A+\cdots}}}$$ have the ...
3
votes
2answers
56 views

Solve $\begin{cases} x + y + z = 2 \\ 2xy - z^2 = 4 \\ \end{cases} $ for x, y, z.

It came to my mind to rewrite the expression above as $$\begin{cases} x + y = 2 - z \\ 2xy = (2 - z)^2 + 4z \\ \end{cases} $$ and see if there any restrictions on the values of the variables occur. ...
0
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1answer
27 views

System of equations problem?

In a chemistry class, 3 liters of a 4% silver iodine solution must be mixed with a 10% solution to get a 6% solution. How many liters of the 10% solution are needed? Equation: .10x + .04(3-x) = ...
1
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5answers
170 views

Find $x$ if $\frac {1} {x} + \frac {1} {y+z} = \frac {1} {2}$ [on hold]

I found this question from past year's maths competition in my country. I've tried any possible way to find it, but it is just way too hard. Find $x$ if \begin{align}\frac {1} {x} + \frac {1} ...
2
votes
2answers
103 views

Systems of equation with only 1 equations?

So this is a system of equations problem only there's 1 equation as far as I could tell? Roberto invested some money at 7% and then invested 2000 more than twice this amount at 10% His total anual ...
0
votes
0answers
23 views

Existence and uniqueness of a pde solution

I have the PDE system: $\frac{\delta}{\delta t}u(t,r)=-\int_0^1 H(|r-r'|)v(t,r')dr'u(t,r)$ $\frac{\delta}{\delta t}v(t,r)=\int_0^1 H(|r-r'|)v(t,r')dr'u(t,r)-v(t,r)$ $x(0,r)=\rho(r), ...
2
votes
2answers
29 views

Coupled second-order differential equations

I am trying to solve the following system of coupled ODEs: \begin{align} -x^2 f'' - 3xf' + (1-2a)f - (a+1)x^2g'' + (2-4a)xg' + (4a-2)g &= 0,\\ (a-1)x^2 f'' + (4a+2)xf' + (12-6a)f + 12xg' + ...
3
votes
1answer
35 views

Cramer Rule Over Finite Field

Let $A=\pmatrix{4&2\\ 0&1},\ b=\pmatrix{5\\ 3}$ and $A\pmatrix{x_1\\ x_2}=b$ over the field $\mathbb Z_7$. What is $x_1$? So we need to calculate $$x_1=\frac{\det(A_1)}{\det(A)}$$ ...
-4
votes
0answers
27 views

Simultaneous Equation - no solution and many solutions [closed]

$$mx + 3y = 2,\\ 12x = my = 2m - 8$$ Find values for $m$ which there are a) no solutions b) infinitely many solutions
0
votes
2answers
50 views

System of equations - What's wrong with my solution?

The system of equations below can be solved by substitution or elimination. I understand the official solution to this problem, which I will provide below. I'd like to understand why my initial ...
0
votes
3answers
32 views

What is the solution to this system?

Capital letters indicate constants and lowercase letters indicate variables. I am interested in solving for $\{a,b,c,d,e,f\}.$ How would I go about doing this by hand / what is the solution? $$ ...
1
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0answers
29 views

Uniqueness of the solution of a PDE system

If I have the following PDE system: $\frac{\delta}{\delta t}x(t,r)=-\int_0^1 G(|r-r'|)y(t,r')dr'x(t,r)$ $\frac{\delta}{\delta t}y(t,r)=\int_0^1 G(|r-r'|)y(t,r')dr'x(t,r)-y(t,r)$ $x(0,r)=a(r), ...
0
votes
1answer
21 views

number of solution of system of equations

Prove or provide a counterexamples: $A$ is a $m\times n$ matrix (1) If there exists a vector $b$ such that $Ax=b$ does not have any solution, then $Ax=0$ has infinitely many solutions when $n>m$. ...
2
votes
0answers
39 views

Is this system of inequalities (and equality) tractable?

I have some real parameters here. The $\mu_i$ - for $i=1,2,3,4,5$ - are 'convex coefficents' in that $\mu_i\geq 0$ and $\sum_{i}\mu_i=1$. The $x$ and $z$ are such that $x^2+z^2\leq 1$. The ...
4
votes
0answers
40 views

Why is $\frac d{dt}((\xi \alpha)^{-1})=\frac{-1}{(\xi \alpha)^2} \frac d{dt}(\xi \alpha) = \frac{\partial \lambda_2}{\partial w_1} \xi^{-1}$?

My question concerns the proof of Theorem 2 in §11.3 of PDE Evans: THEOREM 2 (Riemann invariants and blow-up). Assume $\mathbf{g}$ is smooth, with compact support. Suppose also the genuine ...
2
votes
2answers
62 views

Non-linear system of equations

Solve following system of equations over real numbers: $$ x-y+z-u=2\\ x^2-y^2+z^2-u^2=6\\ x^3-y^3+z^3-u^3=20\\ x^4-y^4+z^4-u^4=66 $$ This does not seem as hard problem. I have tried what is obvious ...
1
vote
3answers
96 views

Solving a system of five polynomials

I am trying to solve the following system of equations for tuple $\left(a,b,c,d,t\right) \in \mathbb{R}^{4} \times [0,1]$, with parameter $\ell\in\mathbb{R}$. $$ \begin{eqnarray} a\frac{t^{2}}{2} - ...
0
votes
1answer
35 views

Linear System of Equations [closed]

City and Country Cycles sells two kinds of bicycles, mountain bikes and racing bikes. They have $63,000 to spend on new ...
1
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0answers
33 views

A question about a system of PDE

It is well known that under suitable conditions, the symmetry of mixed second partial derivatives reads: $$\frac{\partial^2 f}{\partial x \partial y}=\frac{\partial^2 f}{\partial y \partial x}.$$ ...
2
votes
1answer
33 views

A general method for solving systems of quadratic equations

For linear systems we have general methods (i.e. Gauss elimination). Is there a general method for solving systems of quadratic equations with many variables? I heard about Groebner bases; is there ...
0
votes
1answer
23 views

consistency of solution question

Let $A, B$ be $n\times n$ matrices and $c, d$ be $n \times 1$ vectors such that the matrix equations $$Ax = c$$ $$Bx = d$$ are consistent, i.e., each equation admits a solution. Can we conclude that ...
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votes
3answers
71 views

$ x+y = 1 $ and $ \frac{1}{x} + \frac{1}{y} = 1 $ Solve $ x^3 + y^3 $ [closed]

$x$, $y$ are complex numbers, $x$ and $y$ aren't $0$. $$ x + y = 1 $$ $$ \frac{1}{x} + \frac{1}{y} = 1 $$ $$ x^3 + y^3 = ? $$ Thank You!
4
votes
1answer
72 views

Another troubling system of equations

I've been working on solving some linear equations arising from different optimization problems, but I keep getting stuck. Right now I have the problem below: I am trying to solve the system of ...
3
votes
5answers
74 views

Using equation to find value of $1/x - 1/y$

$$\left(\frac{48}{10}\right)^x=\left(\frac{8}{10}\right)^y=1000$$ What is the value of $\frac{1}{x}-\frac{1}{y}$? I have already used that when $48$ divided by $10$ then it becomes $4.8$ and when $8$ ...
0
votes
0answers
18 views

What is the best time complexity for this case?

I only want to know if the following system has any integer solution or not. Actually, I do not need to know the solution(s), and only need to know the answer of question "Does the system have any ...
0
votes
0answers
16 views

Set of 3 inequations involving 3 unknowns with a maximum

I am capable of finding a relation between unknowns x, y and z involved in this set of 3 inequations: $\begin{cases} ax - y - z \leq x \\ -x + by - z \leq y \\ - x - y + cz \leq z\end{cases}$ This ...
1
vote
0answers
23 views

Given a set of arbitrary data, is it possible to model this data using differential functions.

Problem At the moment, I have a problem with seven variables: $S, A_1, A_2, R_1, R_2, P_0, P_1 $ and $P_2$. Each of these variables draws a smooth line through time. My question is, is there any ...
4
votes
3answers
129 views

How to solve a system of logarithmic equations?

I need to create a function with the following properties: $$f(1)=1$$ $$f(65)=75$$ $$f(100)=100$$ Additionally, the function needs to grow logarithmically. So that gives three equations: $$A \cdot ...
2
votes
0answers
19 views

$L$-existential and $L$-diophantine

Could you explain to me the last sentence: "Whenever we want to stress dependence on the language, we will use the self-explanatory terms and $L$-existential and $L$-diophantine" ? What does ...
1
vote
1answer
49 views

What does the code do and what ODE is that?

This exercise I came across asks what kind of method of solving ODE is that: ...
1
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1answer
35 views

Equation for spacing of elements on the edge of a circle

I'm trying to come up with an equation which, given an index within an arbitary number of elements (the most natural example would be 12, as in 12 numbers on a clock), along with an arbitrary radius, ...
3
votes
2answers
64 views

Solve $x+y+z=1; x^2+y^2+z^2=35; x^3+y^3+z^3=97$

It may be surprising that I can't get any analytical way of verifying that one of the solutions of $$x+y+z=1$$ $$x^2+y^2+z^2=35$$ $$x^3+y^3+z^3=97$$ is $x=-1, y=-3$ and $z=5$. Although it may be ...
1
vote
0answers
53 views

system of non-homogeneous advection equations

I would like to solve this system \begin{equation} \left\{ \begin{array}{lll} u_t+b_1 u_x=(r+l_1)u-l_1v,\\ v_t+b_2 v_x=(r+l_2)v-l_2u,\\ \end{array} \right. \end{equation} First , I would like to ...
0
votes
1answer
19 views

Solving a system of equations with an absolute value term

$x$ and $y$ are two integer numbers and $x \geq y$. The values of $x$ and $y$ are positive or negative integers. When the sum of these two numbers are multiplied by $y$ we obtain $P$ and when the ...
0
votes
0answers
37 views

How to find a formula for ratios?

I don't know if this is the correct section to post this, but here it goes. I recently got involved with hydroponics, and to feed the plants I've installed a system with a pump that delivers a ...
0
votes
0answers
129 views

Second order coupled differential equations

I am trying to solve two coupled ordinary differential equation. $x''+Ax'+By'+Cx+Dy=U$ ; $y''+Ex'+Fy'+Gx+Hy=V$ ; $A,B,C,D,E,F,G$ & $H$ are constants, $U,V,x$ and $y$ are function of time. All ...
2
votes
2answers
70 views

Solution to system of linear ODE's

Let $\Delta_n$ be the closed unit simplex in $\mathbb R^n$. For any $a,b \in \Delta_n$, define the differential equation: $$ a'(u) = b-a(u) \quad\quad\quad a(0) = a $$ How does one go about solving ...
1
vote
1answer
22 views

System of Linear Equations 2 variables

A theater sold 160 children’s tickets and 90 adult tickets. If the theater made $1,600 from the sales of the tickets, what were the prices of each ticket? My set up is: ...
1
vote
1answer
51 views

Mapping the intersection of hyperplanes/simplex to lower-dimensional unit-simplex

Suppose I have an object in $\mathbb{R}^5$ described by: $$x_1+x_2+x_3+x_4+x_5=1$$ $$x_1+2x_2+3x_3+4x_4+5x_5=6$$ $$x_1+7x_2+8x_3+9x_4+10x_5=11$$ $$x_1,x_2,x_3,x_4,x_5 \geq 0$$ Is there a way that I ...
1
vote
1answer
21 views

Given two variables and their ranges, get a third value.

I'm building a model but I got stuck at this: I have $x,y$ whose ranges are ($10,000$ to $2,000,000$) and (1 to 36) respectively. Also I have a z that ranges from 16 to 30. I know their relations in ...
1
vote
1answer
29 views

Find the end points of a line segment in 3D space

I have a line segment in 3 dimensional space (x,y,z), and I want to find the 2 endpoints of this line segment. Is there a systematic way of doing this? To be specific, I have the line described by ...
-2
votes
2answers
61 views

how to solve nonlinear system of equations

I have $A, B, C, D, E, F.$ I want to calculate a and b from the following system of equations: I know I should solve this system using $3$ equations and $3$ unknowns, but it is not linear. can any ...