System of equations Definition and 285 Threads

$a,\,b,\,c$ are integers that satisfy the system of equations below: $a^2b+b^2c+c^2a=2186$ $ab^2+bc^2+ca^2=2188$ Evaluate $a^2+b^2+c^2$.

Find all real numbers $p,\,q,\,r,\,s$ that satisfy the following system of equations: $spq+sp+pq+qs+s+p+q=9$ $rsp+rs+sp+pr+r+s+p=9$ $qrs+qr+rs+sq+q+r+s=9$ $pqr+pq+qr+rp+p+q+r=1$

I am doing critical points and using the second derivative test (multivariable version) Homework Statement f(x,y) = (x^2+y^2)e^{x^2-y^2} Issue I am having is with the system of equations to get the critical points from partial wrt x, wrt y The Attempt at a Solution f_{x} =...

x^2-13xy+12y^2=0 (1) x^2+xy=156 (2) What I have so far: x^2+xy=156 xy=156-x^2 y=(156-x^2)/x) Plugged y=(156-x^2)/x) into (1): x^2-13x(156-x^2)/x)+12(156-x^2)/x)^2=0 For 1st half I Multiplied x to -13x in order to get the same denominator so I can multiply it to (156-x^2)/x)...

I have a 3 variable system of equations (no solution) and am trying to solve for variables of an Ax = b to be as close to b as possible without changing A. 28446757643x + 82500000y + z = 13557300 283009432x + 283009432y + z = 10264100 14180045548x + 82500000y + z = 3651510 I am...

solve the following system of equations in real a,b,c,d $a+ b =8 $ $ab + c +d = 23 $ $ad + bc = 28$ $cd = 12$

Hey! :o I have the following in my notes: $$u_t+A(x,t,u)u_x=b(x,t,u) \ \ \ \ \ \ \ \ \ \ (1)$$ $$u=(u_1, \dots, u_n), b=(b_1, \dots, b_n)$$ $$A=[a_{ij}], i,j = 1, \dots, n$$ We set the question if there are characteristic directions at the path of which the PDE system $(1)$ is reduced to an...

Here is the question: I have posted a link there so the OP can view my work.

Homework Statement It's a verbal problem. It goes like this: "Peter needs to buy some screws: large, medium, and small. He goes to the hardware store and orders 100 screws for a total of $100. For each large screw he was charged $5.00, $1.00 for each medium one, and $0.05 for each small one...

If a system of first-order ODEs like ##\frac{d\vec{r}}{dt}=A\vec{r}## have as solution ##\vec{r} = C_1 \exp(\lambda_1 t)\hat{v}_1 + C_2 \exp(\lambda_2 t)\hat{v}_2## (being λ the eigenvalues and v the eigenvectors), so, given a system of second-order ODEs, like ##A \frac{d^2 \vec{r}}{dt^2} + B...

Homework Statement Let (**) \begin{matrix} a_{11}x_1 & + & \ldots & + & a_{1n}x_n & = 0 \\ \vdots & & & & \vdots\\ a_{m1}x_1 & + & \ldots & + & a_{mn}x_n & = 0 \\ \end{matrix} be a system of m linear equations in n unknowns, and...

I am studying a system described by a set of first order linear differential equations as can be seen on the attached picture. Now I know that to solve this analytically for a given N, N denoting the matrix size, one has to find the eigenvalues of the given matrix, which translates into finding...

I have attached a photograph of my problem to save time on typing the question I have done the first part to obtain the expression for equilibrium bond length and in the second part I solved that equation for A and substituted it into my binding energy equation and obtained an answer with the...

Consider the system of equations: $p+8q+27r+64s=1$ $8p+27q+64r+125s=27$ $27p+64q+125r+216s=125$ $64p+125q+216r+343s=343$ Evaluate $p+q+r+s$ and $64p+27q+8r+s$.

Find all ordered triples $(x,\,y,\,z)$ that satisfy the following system of equations: $xy+z=6$ $yz+x=6$ $zx+y=6$

Solve in real numbers the system of equations $(3a+b)(a+3b)\sqrt{ab}=14$ $(a+b)(a^2+14ab+b^2)=36$

Homework Statement I have two equations with two unknowns. I know m, F, R, r and I. I need to find a and f. m = 2 F = 28 R = 0.25 I = 0.0625 r = 0.1875 I know the ultimate answers are a = 16\frac{1}{3} and f = 4\frac{2}{3} Homework Equations (1) Fr-fR=I\frac{a}{R} (2)...

Solve the following system for real values of $a$ and $b$: $2^{a^2+b}+2^{a+b^2}=8$ $\sqrt{a}+\sqrt{b}=2$

Hello, I'm working with a system of equations that has an infinite recursion function, and am wondering if its possible to simplify or remove the recursion in terms of the other functions in the system. Any insight into the framework or family of this system is appreciated. Given two...

Homework Statement Solve this system of equations for x and y. v=x+y v^2=x^2+y^2 Homework Equations The quadratic formula: x = (-b +/- sqrt(b^2-4*a*c))/(2*a) The Attempt at a Solution A TA gave the following advice: "Make y the subject of the first equation. Find y2 in terms of v and x...

I've been having a difficult time with system of equations I was wondering if I could have some assistants with system of equations. Here's the question Question: Keller industries' profits were up $ 20,000 this year over last year. This was an increase of 25%. a. Let T represent the profit...

I have big problems with an equation system. It's been a long time since I worked with these type of problems and it would be wonderful if I could get an full solution of this or some similar problem. Decide for all real a and b, the number of solutions to the equation system. I...

Hello, I've been trying to solve a system of equations but I'm getting a lot of troubles when I tried to insert inside a matrix a numeric variable. This is my code. I've tried both schemes, i.e., (1) introducing all elements of the matrix by hand (real numbers) and (2) introducing numeric...

Hello all, I am working on this system of equations, and I do not get the same results as they appear in the final solution in the book, need your assistance here...this is the question: Discuss the solutions of the equation system: \[\begin{matrix} ax_{1}+bx_{2}+2x_{3}=1\\...

Homework Statement x + y+ z = 0 3x + 2y -2z = 0 4x + 3y -z = 0 6x + 5y + z = 0 Homework Equations The Attempt at a Solution I put the equations into a matrix and reduced to RREF. This is what I end up with: x - 4z = 0 y + 5z = 0 The other two rows in the matrix are all...

Homework Statement Under what condition will the following system have a unique solution? x -y +2z = 1 ax -ay +4z = 2a x +y +az = 4 Note: a is a parameter. The Attempt at a Solution I know I'm supposed to solve by turning this into the identity matrix by I really have no idea...

I need your help for solved this. :confused: X^2+y^2=9 (x+3)^2+(y-3)^2=9 Please help me.

Say that I have 2x+2yz=0 2y+2xz=0 and 2z+2xy=0 how would I use matrix methods to solve this system of equations? I know you can just look at it and easily figure out what the critical points are but I want to do it the safe way. Or is using the matrix method not the easiest way here? For...

Homework Statement It's a longer problem but all that's left is: y = k^2 \frac{1-cos(\theta)}{2} x = k^2 \frac{\theta - sin(\theta)}{2} I want to find a k that solves the equations for the point (x, y) = (x_0, y_0) The Attempt at a Solution I manipulated them to get two expressions for k...

Solve the following system: $x-y=1-z$ $3(x^2-y^2)=5(1-z^2)$ $7(x^3-y^3)=19(1-z^3)$

Homework Statement Solve simultaneously: 6(x + y) = 5xy, 21(y + z) = 10yz, 14(z + x) = 9zx Homework Equations -The Attempt at a Solution Obviously one of the solution is (0,0,0) But I'm more interested in finding the other. Expanding these three equations , I get - 6x+6y=5xy 21y+21z=10yz...

It's fairly straight forward to find information on how to solve a system of equations like this: 2x + 3y + 4z = 1 3x + 4y + 3z = 2 4x + 5y + 3z = 3 It has numerical constants in front of each term. You could use Gaussian elimination and solve for one, infinite, or no solutions. (The above...

$a,b,c,\in N$ $( a −b)(b − c )(c + a ) = −90$ $( a − b)(b + c)(c − a ) = 42$ $( a + b)(b − c )(c − a ) = −60$ $ find :\,\, a,b,c$

Calculation of Real $(x,y,z)$ in $x[x]+z\{z\}-y\{y\} = 0.16$ $y[y]+x\{x\}-z\{z\} = 0.25$ $z[z]+y\{y\}-x\{x\} = 0.49$ where $[x] = $ Greatest Integer of $x$ and $\{x\} = $ fractional part of x My try:: Add $(i) + (ii)+(iii)$ $x[x]+y[y]+z[z] = 0.9$ Now I did not Understand How Can I...

Homework Statement I have a system of two equations: 3*x^2 - x + 3*y^2 = 0 2*x^2 - y + 2*y^2 = 0 Homework Equations The Attempt at a Solution I don't know how to express one with the other.I mean I can either have x = 3*y^2 + 3*x^2 or y = y = -2*y^2 - 2*x^2 and in both cases it...

Homework Statement This is the problem: |4(x+2) - 7(x-y) = 7 |7(x+y) + 10(x-2) = 79 I need to solve this, I'm not quite sure what to do, the operators in the brackets are different, so even if I multiply by -1, if the operator in front of one variable changes, the other one will...

Hello everyone! I have a question on whether a system of equations can be classified as linear. I have the following matrix: \begin{equation} \left[ \begin{array}{c} S_t(1) \\ S_t(2) \\ \vdots \\ S_t(\omega_N) \end{array} \right] = \begin{bmatrix} f(x_1, x_2, 1) & f(x_2, x_3, 1) & \cdots &...

Solve the equation m\frac{d^{2}x}{dt^{2}} + c\frac{dx}{dt} + kx = (ax + b)^{2} + c^{2} for the constants m, c, k The right hand side a, b, and c are arbitrary digits. For me they are a = 2, b = 3, and c = 8. The problem recommends creating a linear system of equations for me to solve. This...

So we are given two equations: $$ \ddot{x} - \dot{x} - x = cost (t) $$ and $$ x(t) = a sin(t) + b cos(t) $$ The question asks to find a and b. How would one go about doing this? I thought maybe substituting the $$ cos(t) $$ from equation 1 into equation 2 would work but then what...

Hi all, I'm stuck on a system of equations I am left with at the end of a dynamics problem. a=-b+v x=-b+vcos(30) y=vsin(30) 171.5=20b^2+5a^2 a^2=x^2+y^2 10x-40b=0 All in degrees. I know I have an extra equation, but I thought I'd include it in case it is easier to solve with a...

Homework Statement An alpha particle traveling with a kinetic energy of 5.5 MeV and a rest-mass of 3727.8 MeV/c^2 strikes a gold atom with a rest-mass of 183,476 MeV/c^2. -The gold atom is initially at rest -The alpha particle deflects perpendicular to the horizontal in the after state...

Solve the system: $x^3+3xy^2+49=0$ $x^2-8xy+y^2=8y-17x$ Hi all, I found this problem interesting and I think you may find it interesting too. I have solved it and am of course interested in seeing other approaches. I will post my solution in a few days, so that everyone interested can have...

Problem: Solve the system: $\displaystyle \sqrt{3x}\left(1+\frac{1}{x+y} \right)=2$ $\displaystyle \sqrt{7y}\left(1-\frac{1}{x+y} \right)=4\sqrt{2}$

Hi, I need to solve the following system of equations: qa = fa (qa, qb, qc, qd) qb = fb (qa, qb, qc, qd) qc = fc (qa, qb, qc, qd) qd = fd (qa, qb, qc, qd) where all the variables and functions are complex. However, there are some additional constraints for the variables, let's call...

I am having a bit of trouble solving the following system of equations. I know what numbers solve the system, but I can only do so using a computer, such as WolframAlpha. The equations , for those interested, are the four partial derivatives for a Lagrange Multiplier. The four equations are as...

Solve for a T - mg = -ma T = Ma They get a = mg / (M + m)...how? I get up to this point... Ma + ma = mg

I was trying to understand why in the attached equations when they divided to get F_B alone it wasn't 2B. Thanks

Hello :) I'm learning about systems of equations and substituting and stuck on this problem. It seems pretty simple but I keep getting trampled by small things and I can't find out what I'm doing wrong. 6y=x+18 2y-x=6

I've been trying to get out this question for a while now: ai) Show that (x,y,z) = (1,1,1) is a solution to the following system of equations: x + y + z = 3 2x + 2y + 2z = 6 3x + 3y +3z = 9 aii) Hence find the general solution of the system b) Express 2x^2 + 3/(x^2 + 1)^2 in partial...

Homework Statement Hello everyone. I'm trying to solve a non linear 11x11 system. (for eliminate harmonics in a power inversor) I used Excel's Solver but it didn't work. (Solver couldn't solve the system). Then I found fsolve (a scilab function) but again it didn't work I will attach...