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
19 views

Help on Solutions to Systems of Equations

Here is a screenshot: http://imgur.com/gallery/Wh6ksgO/new I was looking at my Linear Algebra quiz solutions and I saw the following: "Thus from RREF, we can see the system if consistent and contains ...
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votes
1answer
24 views

Learning to solve complex inequalities in many variables

below is a very specific inequality problem. I would like to know how to solve it so I can apply it to more complex problems. The equations are as follows: $$3.5x−2.5y−3z=A$$ $$−7.5x+3.75y+5.25z=B$$ ...
-1
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0answers
21 views

Trying to solve a simultaneous equation… [on hold]

Trying to solve the following but don't think I have enough data. The overall aim is to find the conversion rate of aggregator customers. Here is the data set: Direct quotes: 170 Direct accepts: ...
0
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3answers
34 views

Finding the kernel of a linear map

Our exercise is to find all solutions to the equation $Ax = 0$, among others for the following matrix $$A =\begin{pmatrix} 6 & 3 & -9 \\ 2 & 1 & -3 \\ -4 & -2 & 6 ...
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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
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3answers
52 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: $$xy+1=3(x+y) $$
2
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1answer
63 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; $$x(0) = 0$$ ...
1
vote
1answer
72 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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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.
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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
1answer
43 views

My attempt regarding finding critical ponts of $(\cos x)(\cos y)(\cos(x+y))$

Given this problem Restrictions on $x$ any are that $x\in[0,\pi]$ , $y\in[0,\pi]$ I have $f_x=-(\cos y)({\sin(2x+y))}--------*$ $f_y=-(\cos x)(\sin x+2y)-----------**$ So from $*$ I get either ...
0
votes
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 ...
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votes
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
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. ...
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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? ...
2
votes
1answer
577 views

Numerical techniques for solving systems of first-order semi-linear hyperbolic PDEs in two variables

I need to solve such systems of PDEs numerically and I'm wondering what the "standard" method (if there is one) is. The systems I'm interested in have the form: $\frac{\partial F_i}{\partial t} + ...
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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 ...
0
votes
1answer
40 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 ...
0
votes
2answers
67 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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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 ...
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votes
2answers
23 views

System of equation problem [closed]

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
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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2answers
48 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 $a, b, c, d, e$ ...
2
votes
4answers
147 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
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
vote
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 ...
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 ...
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 ...
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4answers
126 views

I am thinking of a two digit number… (System of Equations Question)

I am thinking of a two digit number. If the digits of my number are reversed, the new number is 36 greater than my original number. If the tens digit of my original number is doubled and the units ...
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 ...
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
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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 ...
2
votes
3answers
72 views

Finding maximum points by constrain optimization (multivariable calculus)

Find the maximum value of the function $f(x,y)=x^2+y^2+2x+y$, on the closed disc (the circle together with the region inside the circle) of radius 2, centred at the origin. What i tried I know that ...
8
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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 = ...
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} ...
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) = ...
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 ...
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' + ...
0
votes
2answers
30 views

Linear Equations over $\{0,1\}$ with addition considered over $\mathbb Z$

Is there any way to solve a system of linear equations with both the coefficients and variables coming from $\{0,1\}$ but where addition is considered over the non-negative integers, not ...
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), ...
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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2answers
366 views

Phase Plane Analysis

Classify the fixed point at the origin and sketch an accurate phase portrait for the following system: $$\left\{\begin{matrix} \dfrac{dx}{dt}=36x-16y\\ \dfrac{dy}{dx}=-3x+28y \end{matrix}\right.$$ ...
4
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1answer
830 views

How to solve coupled linear 1st order PDE

It is fairly straight forward to solve linear 1st order PDEs by the method of characteristics. For example, if $\partial_tf+a\partial_xf=bf$ , we have that $\dfrac{df}{dt}=bf$ on the characteristic ...
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 ...
3
votes
1answer
47 views

Intuitive Explanation For Why Dependent Equations Contain No Added Information?

I've always been taught that because dependent equations contain no added information they can be deleted without effecting the solution set. Now this makes sense to me if an equation is a constant ...
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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), ...
1
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} - ...
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? $$ ...
2
votes
2answers
63 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 ...