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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0answers
14 views

Binary solutions of multivariate polynomial system in special (factored) form.

In my personal research I've run into a system of multivariate polynomials (with coefficients in a field). I am aware that there is no polynomial time algorithm (in the number of indeterminates) for ...
0
votes
3answers
51 views

Solving this Cubic equation

$(x^2+y)(x+y^2)=(x+y)^3$ Can $x^2+y^2$ attain values $2$ and $13$? How to approach this question I tried solving this equation and couldn't solve after this: $$xy+1=3(x+y) $$
1
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1answer
68 views

Finding $a^{2014} + b^{2014} + c^{2014}$ given some conditions on $a,b,c$.

I came across this problem: "Let $a$, $b$, $c$ be nonzero real numbers that satisfy the conditions : $$a + b + c = 9,\\\mathrm{and}~ab + bc + ca = 27 $$ Calculate $$a^{2014} + b^{2014} + ...
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votes
2answers
15 views

coordinate question 2 [on hold]

A ray of light passing through the point(1,2) reflects on the x axis at point A and the reflected ray passes through the point(5,3) find the coordinates of A.
-1
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0answers
23 views

System of Equations, 3 Unknowns intersecting along a line parallel to the line where the other pairs intersect

I have this system of equations with 3 unknowns: Ax + By + Cz = D 5x + 3y + 2z = 4 -14x - 16y = 4 I need to find the values for A, B, C and D that will make it inconsistent and have each pair of ...
0
votes
3answers
47 views

Add or subtract something to a number to reduce it to the range 0 to 24

I'm developing a C++ program and I need to find a formula that given a number to reduce and a limit number, get a value between 0 and this limit number. I don't know if it is allow to put C++ code ...
-3
votes
0answers
23 views

Systems of equation [on hold]

Mr. Sharma's chemistry class needs to make a 50mL solution that is 30% acid from two solutions, one of which is 10% acid and one of which is 35% acid. How many mL of the 10% solution should they use? ...
0
votes
2answers
66 views

Find all the possible real values for $a,b,c,d$.

Let pairs $(a,c)$ and $(b,d)$ be roots of the equations $x^2 + ax - b = 0$ and $x^2 + cx + d = 0$ respectively. Find all possible real values for $a,b,c,d$.
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votes
1answer
39 views

Find function by 2 tangents and 2 points

I am looking for explicit function descriptions $F_1(s)$ and $F_2(s)$, following the line plotted. The line is just a description, but $F_1$ should never exceed $F_m$ and start at $s_0$ with a tangent ...
2
votes
3answers
25 views

Question on Quadratic Equations.11

Base of an equilateral triangle lies along the line $$9x+40y-50=0$$ and its vertex opposite to the base lies on the line $$9x+40y+32=0$$ Find the length of the side of the triangle and also find its ...
1
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2answers
61 views

How to solve this equation numerically???

The equation is given by $$ \sum_{n=1}^N \min(\gamma, \beta a_n)=N$$ where $\beta$ is the variable with $\beta\in[0,\sqrt\gamma/\min(a_n\mid a_n>0)]$, $ \gamma $ is a constant with ...
-1
votes
2answers
23 views

System of equation problem [on hold]

Let $A$ be a $3 \times 3$ matrix made from the variable coefficient of the following system. Let $B$ be a $3 \times 1$ matrix made from the coefficients of the right hand side. Solve the system by ...
2
votes
1answer
62 views

Is there a numerical solution for a system of three 1st order nonlinear ODE?

How would I go about solving the following system of non-linear ODEs for $x(t), y(t), z(t)$ $$x' = y $$ $$y'=\sin(x)+z$$ $$z'=y-z$$ I have the following initial conditions; $$x(0) = 0$$ ...
2
votes
3answers
83 views

Solve the equation $4\sqrt{2-x^2}=-x^3-x^2+3x+3$

Solve the equation in $\Bbb R$: $$4\sqrt{2-x^2}=-x^3-x^2+3x+3$$ Is there a unique solution $x=1$? I have trouble when I try to prove it. I really appreciate if some one can help me. Thanks!
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votes
1answer
18 views

Solving Equations system question

We get this equation and need to solve Solve in $\mathbb{Z} $ the given equation $ y(y -x )(x+1) = 12\ $
1
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1answer
48 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 ...
1
vote
2answers
47 views

Solving two diophantine equations.

Find at least one 5-tuple of positive integers which satisfy the following two equations $$a^2-d^2=3(b^2-c^2)$$ $$e^2-b^2=3(d^2-c^2)$$ such that no three of the 5 positive integers $a, b, c, d, e$ ...
0
votes
2answers
36 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
146 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
votes
0answers
27 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
vote
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
112 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
52 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
56 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
59 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
votes
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
vote
5answers
173 views

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

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
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0answers
25 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
30 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 $$x_1=\frac{\det(A_1)}{\det(A)}$$ ...
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0answers
29 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
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2answers
55 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
30 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
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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
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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 ...
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vote
3answers
97 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} - ...
1
vote
0answers
34 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
72 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
74 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 ...