# Tagged Questions

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### 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 ...
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### 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 ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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) ...
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### 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.
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### 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 ...
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### 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.
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### 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 ...
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### 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 ...
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 $y$ ...
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 ... 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 ... 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 ... 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 ... 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 ... 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 ... 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$$The parameters are: k,L,d,q,m,g The ... 1answer 71 views ### Infinite set of equations Consider an infinite set of equations in an infinite number of variables, if every finite subset of equations has a solution, must the entire set of equations have one? Each equation contains a ... 3answers 58 views ### Given system of equations a+b = 2, ab=4 solve a^2+b^2=? and a^3=? I am trying to solve a^2+b^2 and a^3 given a+b = 2, ab=4. I have the key with the answers a^2+b^2=-4 and a^3=-8 but am wondering which steps to take to get to that answer. My understanding ... 1answer 43 views ### How to solve the equations system? I have a system of equations that I don't know how to solve. 1) x = a - y ; 2) y = b \times sin(90 -z); 3) z = \dfrac{(x - c )^2 }{b^2 \times e^2} a, b, c, d and e are known. How can I ... 4answers 60 views ### solving the system solve the system :$$ y+|x-2|=3 $$,$$ |x+y|= m $$graphicly when m equals 6. I can easily (realtively) skecth the first graph , however, how the bloody hell do you sketch |x+y|= 6?? 1answer 88 views ### how to solve these equation? For a , b , x , y are members of \mathbb{R} If ax+by=3\\ax^2+by^2=7\\ax^3+by^3=16\\ax^4+by^4=42 then ax^5+by^5=? a lot of thanks for all comments 4answers 753 views ### How find the value of the x+y Question: let x,y\in \Bbb R , and such$$\begin{cases} 3x^3+4y^3=7\\ 4x^4+3y^4=16 \end{cases}$$Find the x+y This problem is from china some BBS My idea: since ... 0answers 17 views ### bounds of solution to the system of nonlinear equations I have a system of nonlinear equations: \begin{eqnarray*} F_1(x,y) &=& 0,\\ F_2(x,y) &=& 0, \end{eqnarray*} where F_i(x,y) with i=1,2 are continuosly differentiable in (x,y). ... 1answer 49 views ### How can I write a system of equations puzzle if given the solutions? (work backwards?) \begin{matrix} a = 12 & b = 6 & c = 5 & d = 1 & e = 0\\ \end{matrix} How can I create a fun puzzle or word problem that would arrive at this solution above? For example, ... 1answer 146 views ### Cyclic system of equations Consider the system of equations$$ \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 ... 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 ... 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 ... 1answer 41 views ### roots of system of nonlinear equations I can't get any solutions beside when x=0\vee y=0 \vee z=0yz-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}$$Can you help ... 1answer 39 views ### Special equation solving I would like to get x from the following function when the y is known and which + means If ... 2answers 19 views ### What is wrong with this technique for proving skew lines? We have the following set of lines:$$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: ... 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 ... 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 ... 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 ... 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? 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 ... 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 ... 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 ... 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 ... 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 $$where the values of \{c_1 \ldots c_n \} and \{ k_1 \ldots k_n \} are known, and x, \{y_1 \ldots y_n \} are ... 0answers 48 views ### Solving a system of 3 variables How to solve or what is the algorithm to solve a system of equations like this:$$\eqalign{ (x +\phantom{3} z)^2 + (y +\phantom{3} w)^2 &= 52\cr (x + 3z)^2 + (y + 3w)^2 &= 296\cr (x ... 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}}$I have been told that since the denominators are irreducible, the ... 3answers 66 views ### Partial fraction decomposition of a complicated rational function Find the partial fraction decomposition of the rational function$\displaystyle \frac{2x^3+7x+5}{(x^2+x+2)(x^2+1)}$I have tried dividing first but keep running into problem after problem, please ... 2answers 64 views ### Solving$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 ... 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 ... 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 ... 3answers 57 views ### Solve the System of Equations in$x$and$y\$
$$x+\frac{3\,x-y}{x^2+y^2}=3 \tag{1}$$ $$y=\frac{x+3\,y}{x^2+y^2} \tag{2}$$