-1
votes
1answer
9 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 ...
1
vote
1answer
30 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
3answers
55 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
39 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
4answers
54 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 $|x+y|= 6$??
3
votes
1answer
85 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
13
votes
4answers
736 views

How find the value of the $x+y$

Question: let $x,y\in \Bbb R $, and such $$\begin{cases} 3x^3+4y^3=7\\ 4x^4+3y^4=16 \end{cases}$$ Find the $x+y$ This problem is from china some BBS My idea: since ...
0
votes
0answers
17 views

bounds of solution to the system of nonlinear equations

I have a system of nonlinear equations: \begin{eqnarray*} F_1(x,y) &=& 0,\\ F_2(x,y) &=& 0, \end{eqnarray*} where $F_i(x,y)$ with $i=1,2$ are continuosly differentiable in $(x,y)$. ...
1
vote
1answer
46 views

How can I write a system of equations puzzle if given the solutions? (work backwards?)

\begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix} How can I create a fun puzzle or word problem that would arrive at this solution above? For example, ...
11
votes
1answer
141 views

Cyclic system of equations

Consider the system of equations $$ \begin{align*} x^2+(1-y)^2&=a\\ y^2+(1-z)^2&=b\\ z^2+(1-x)^2&=c\\ \end{align*} $$ Compute $x(1-x)$ in terms of $a,b,c$. Edit: The question should say ...
1
vote
1answer
46 views

Solving non-linear (convex) systems of equations

I have a system of non-linear equations that takes the following form \begin{align} \left[ \begin{array}{c} y_1 \\ y_2 \\ \vdots\\ y_n \end{array} \right] = \left[ \begin{array}{c} f_1({\bf ...
0
votes
0answers
23 views

Matrices and solving 3 variable systems

The problem is as follows: You sell tickets at school for fundraisers. You sold car wash tickets, silly string fight tickets and dance tickets – for a total of 380 tickets sold. The car wash ...
0
votes
1answer
26 views

How do I modify a system of equations to receive unlimited solutions (SAT Question)

I am sorry that I don't have a specific question (it was on my sat make-up) but I remember a question that went something like 3x + 2y = 26 and another part of the system of equations that I don't ...
1
vote
1answer
41 views

roots of system of nonlinear equations

I can't get any solutions beside when $x=0\vee y=0 \vee z=0$ $$yz-2x\lambda-2x\mu=0\tag{1}$$ $$xz-2y\mu=0\tag{2}$$ $$xy-4z\lambda =0\tag{3}$$ $$x^2+y^2=4\tag{4}$$ $$x^2+2z^2=3\tag{5}$$ Can you help ...
0
votes
1answer
39 views

Special equation solving

I would like to get x from the following function when the y is known and which + means If ...
0
votes
2answers
19 views

What is wrong with this technique for proving skew lines?

We have the following set of lines: $$L_1: \frac{x-2}{1}=\frac{y-3}{-2}=\frac{z-1}{-3}$$ $$L_2:\frac{x-3}{1}=\frac{y+4}{3}=\frac{z-2}{-7}$$ This leads to the following parametric equations: ...
1
vote
3answers
25 views

Simultaneous equations

I keep getting the following equation wrong: Firstly, I solve for y = x - 4, and substitute it in the second equation. Then once I get x from the second equation, I substite it back into the first ...
0
votes
2answers
56 views

software to solve system of nonlinear equations

I am looking for a software to solve system of nonlinear equations. It would be great if the software can satisfy the following requirements It can support symbolic computation. It deals well with ...
0
votes
1answer
58 views

Help solve an equation

I'm preparing for the SAT and tripped over the following problem: $(x-8)(x-k) = x^2 - 5kx + m$ "In the equation above, k and m are constants. If the equation is true for all values of x, what is ...
3
votes
2answers
63 views

A system of equations

Given three equations $x^2+y^2+xy=a$, $y^2+z^2+yz=b$ and $x^2+z^2+xz=c$, how can I solve for $x,y$ and $z$ in terms of $a,b$ and $c$?
0
votes
3answers
31 views

Question about solving systems of equations (Highschool level)

If I am asked to solve a systems of equation, how would I know which method (substitution, or elimination) to use? What set of conditions should I be looking for, or is it that either method should in ...
0
votes
1answer
23 views

Question about solving systems of equations

Is their a universal method to solve systems of equation, eg do methods such as 'elimination' work for ALL types of simultaneous equations (I am specifically referring to 2 and 3 equation simultaneous ...
0
votes
1answer
30 views

Find the height of the dam given angles of a triangle

The top of a dam has an angle of elevation of 1.3 radians from a point on a river. Measuring the angle of elevation to the top of the dam from a point 155 feet farther downriver is 0.8 radians; assume ...
0
votes
1answer
34 views

Finding equations when given new center of a circle

$y = −x + \sqrt{2}$, $y = −x − \sqrt{2}$, $y = x + \sqrt{2}$, and $y = x − \sqrt{2}$. These equations determine lines, which in turn bound a diamond shaped region in the plane. Construct a diamond ...
1
vote
0answers
50 views

find $x$, given $\{c_ix = k_i + y_i\}_{i=[1,n]} $

Given $$c_1x = k_1 + y_1 $$ $$c_2x = k_2 + y_2 $$ $$\vdots $$ $$c_nx = k_n + y_n $$ where the values of $\{c_1 \ldots c_n \}$ and $\{ k_1 \ldots k_n \}$ are known, and $x, \{y_1 \ldots y_n \}$ are ...
3
votes
0answers
47 views

Solving a system of 3 variables

How to solve or what is the algorithm to solve a system of equations like this: $$\eqalign{ (x +\phantom{3} z)^2 + (y +\phantom{3} w)^2 &= 52\cr (x + 3z)^2 + (y + 3w)^2 &= 296\cr (x ...
1
vote
3answers
29 views

Why the linear numerator for fractions with irreducible denominators and constant numerators for reducible denominators? [duplicate]

For example: $\Large{\frac{2x^3+5x+1}{(x^2+4)(x^2+x+2)}}$ breaks down to $\Large{\frac{ax+b}{x^2+4}+\frac{cx+d}{x^2+x+2}}$ I have been told that since the denominators are irreducible, the ...
1
vote
3answers
66 views

Partial fraction decomposition of a complicated rational function

Find the partial fraction decomposition of the rational function $\displaystyle \frac{2x^3+7x+5}{(x^2+x+2)(x^2+1)}$ I have tried dividing first but keep running into problem after problem, please ...
17
votes
8answers
3k views

Kid's homework: 4 equations 5 unknowns? Going crazy!

I'm new here, and I'm hoping someone can help out. My 10 year old son has been set a maths problem, which I can't solve. I've got a PhD in neuroscience and do a fair amount of matlab stuff (data ...
0
votes
1answer
39 views

Solve a system of inequalities

$$\begin{cases} \log_{2}^{2}(-\log_{2}x) + \log_{2}\log_{2}^{2}x \leq 3 & \\-4 |x^2-1|-3\geq \frac{1}{x^2-1}& \end{cases}$$ What I've tried: Make substitution $t=x^2-1$ and solve second ...
1
vote
3answers
56 views

Solve the System of Equations in $x$ and $y$

\begin{equation} x+\frac{3\,x-y}{x^2+y^2}=3 \tag{1} \end{equation} \begin{equation} y=\frac{x+3\,y}{x^2+y^2} \tag{2} \end{equation}
0
votes
4answers
63 views

Solving a logarithmic system of equations

I am working on a test study guide and I can't seem to get the correct answer for this system of equations: \begin{align*} \ln(x) &= 3\ln(y) \\ \ 3^x &= 27^y \end{align*} I'm not ...
0
votes
1answer
18 views

Systems of Linear equations (substitution method) *Got Part A*IDK about Part B*Part C i have no clue?*

Part A: write the equation that represents M................. y=2x-5 Write the equation that represents N.............................. y=3x+2 ( that is right^^^^^) Part B:using the equations you ...
0
votes
1answer
14 views

If M = S, how to isolate a?

So I have to isolate $a$ in $M=S$ $M=1+\dfrac{a}{b}$ $S=a+b$ So, I put it up like this: $1+\dfrac{a}{b}=a+b$ ... right? But then what?
0
votes
1answer
29 views

Intersection of linear and quadratic functions

I've been stuck on some math work and I'm not sure how to do it. It involves finding the point where a quadratic and linear function intersect only once. Determine the value of $k$ such that $g(x) = ...
1
vote
2answers
197 views

Real world situation with System of Equation with 3 variables?

Where do you run into a real world situation involving 3 variables and 3 equations? Can someone think of a specific example from business, etc? I recall taking an operations research course that ...
4
votes
3answers
73 views

Solving Two Equations and Solving

I'm not sure what this is called, but I'll write the problem below. If anyone can help me, as well as tell me where I can get a review of this topic I'd appreciate it. $${\left\{{\begin{align}&2x ...
1
vote
3answers
77 views

$ \frac{x}{4 \ \sqrt{x^2+1}} \ = \ \frac{y}{5 \ \sqrt{y^2+1}} \ = \ \frac{z}{6 \ \sqrt{z^2+1}} $ and $ \ x+y+z \ = \ xyz \ $

Consider the system of equations in real numbers $ \ x,y,z \ $ satisfying $$ \frac{x}{4 \ \sqrt{x^2+1}} \ = \ \frac{y}{5 \ \sqrt{y^2+1}} \ = \ \frac{z}{6 \ \sqrt{z^2+1}} $$ and $ \ x+y+z \ = \ ...
0
votes
3answers
57 views

Solve a system of equations involving two ellipses

Problem #38 asks us to solve the system using either graphing, substitution, or elimination. The only way that I can think of doing this is by graphing. However, is there any easy way to solve this ...
1
vote
3answers
92 views

Solve two equations for $a$ and $b$

\begin{cases} c_2=\dfrac{c_1}{a} \left( \left(\dfrac{c_3}{b}\right)^3 - 1 \right) \\[2ex] b^2 = a^2 + c_3^2 + 2(a)\, (c_3)\, (c_4) \\ \end{cases} I am stuck at this point. Not sure on how to move ...
0
votes
1answer
31 views

Condition number of system of non-linear equations

I've a system of non-linear equations. The system has only two unknowns but 6 equations (thus over-determined). Solving the system of equations are not a problem. However, I need an indication of how ...
0
votes
0answers
21 views

Some solution for a particular system of non-linear equations

I have come across this system of equations where $q>1$ is a real constant, $x_i$ and $y_i$ are real variables and $y_i>0$: $$ \begin{align} 1~~ & = x_0 ~~~~ ~~+ x_1 ~~~~~~~+ x_2 ...
0
votes
0answers
99 views

solving a system of algebraic equations

I'm trying to solve the following system of nonlinear algebraic equations for $q_{e}\in\mathbb{R}^{4}$ $$ ...
4
votes
1answer
62 views

issues with simple algebraic equations

$ab + a + b = 250$ $bc + b + c = 300$ $ac + a + c = 216$ then find $a + b + c = ?$ MY APPROACH: (i) * c , (ii) * a , (iii) * b then we get $abc + ac + bc = 250c$ $abc + ab + ac = 300a$ ...
2
votes
4answers
92 views

Find the equation of a circle passing three points (conics)

Problem: Determine the equation of the circle that passes through three points, $J(-3, 2)$, $K(4, 1)$, and $L(6, 5)$. I thought of using systems like so: $$\left\{ \begin{array}{rcl} (x+3)^2 + ...
4
votes
0answers
29 views

Is there a name for systems of equations with min and max functions included?

In a big project I'm working on, I'm running into systems of equations that look like the following: $$a = \min(b, c)$$ $$b = d^2 + a$$ $$c = \max(a + b, d)$$ Basically, nonlinear systems of ...
1
vote
1answer
118 views

I wonder whether the system of equations and inequations below have a solution.

I wonder whether the system of equations and inequations below have a solution. If there are solutions, what are they? A numerical solution is also desired. $$\begin{cases} ...
1
vote
1answer
78 views

Solve …

This is what I did Can anyone tell me what's wrong me or the question?
1
vote
0answers
19 views

Find a maximal set of independent equations in a system of non-linear equations.

Given a system of non-linear algebraic equations. Is there some general method to find a maximal set of independent equations in this system? For example, $\{x^2+y^2=1, x = y\}$ is a maximal set of ...
2
votes
1answer
49 views

How to solver this equation $\sum_{i=1}^{6}x_{i}x_j=-3,j=1,2,3,4,5,6,j\neq i$

Let $x_{i}\in R,i=1,2,3,4,5,6$ such that $$\begin{cases} x_{1}x_{2}+x_{1}x_{3}+x_{1}x_{4}+x_{1}x_{5}+x_{1}x_{6}=-3\\ x_{2}x_{1}+x_{2}x_{3}+x_{2}x_{4}+x_{2}x_{5}+x_{2}x_{6}=-3\\ ...