0
votes
1answer
63 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
0answers
16 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 ...
4
votes
4answers
492 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
4answers
64 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
44 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 ...
1
vote
4answers
137 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
17 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) ...
3
votes
2answers
36 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
21 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 ...
0
votes
1answer
69 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.
0
votes
3answers
44 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 ...
2
votes
3answers
41 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
22 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
28 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
65 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 ...
0
votes
1answer
37 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 ...
2
votes
0answers
56 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
41 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
17 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
32 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
1answer
71 views

Infinite set of equations

Consider an infinite set of equations in an infinite number of variables, if every finite subset of equations has a solution, must the entire set of equations have one? Each equation contains a ...
2
votes
3answers
58 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
43 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
60 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
88 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
753 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
49 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
146 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
52 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
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
74 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
65 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
24 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
35 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
40 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
48 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
31 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 ...
3
votes
2answers
64 views

Solving $L= \frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}$ priveded $a+b+c=0$

Let $a,b,c$ be such that $a+b+c=0$ and suppose that $$L= \frac{a^2}{2a^2+bc}+\frac{b^2}{2b^2+ac}+\frac{c^2}{2c^2+ab}.$$ Find the value of $L$. I can only see the symmetry of these function ...
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
57 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}