System of equations Definition and 285 Threads

In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single equations, namely as a:

System of linear equations,
System of nonlinear equations,
System of bilinear equations,
System of polynomial equations,
System of differential equations, or a
System of difference equations

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  1. anemone

    MHB Solving the System of Equations for $a^2+b^2+c^2$

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

    MHB System of Equations: Find Real Numbers $p,q,r,s$

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

    System of equations (multivariable second derivative test)

    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} =...
  4. H

    MHB Solving System of Equations using Substitution or Elimination

    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)...
  5. Z

    Approximately solve system of equations

    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...
  6. kaliprasad

    MHB Solve System of Equations: a+b, ab+c+d, ad+bc, cd

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

    MHB Need explanation-hyperbolic system of equations

    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...
  8. MarkFL

    MHB David's Math: Solving a Non-Linear System in 2 Variables

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

    Building a system of equations

    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...
  10. J

    Solution for system of equations

    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...
  11. C

    Linear system of equations with non-trivial solutions

    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...
  12. A

    Solving Linear Differential System: Eigenvalues & Exact Solutions

    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...
  13. KiNGGeexD

    Interatomic potential and binding energy system of equations

    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...
  14. anemone

    MHB System of Equations II: Evaluate p+q+r+s & 64p+27q+8r+s

    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 $64p+27q+8r+s$.
  15. anemone

    MHB The Time Difference Between Posts

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

    MHB System of Equations: Real Number Solutions

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

    System of Equations with Two Unknowns, Algebra Help

    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)...
  18. anemone

    MHB Solving a System of Equations for Real Values of $a$ and $b$

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

    Simplifying an Infinite Composite Recursion in a System of Equations

    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...
  20. K

    System of Equations Involving a Quadratic: Have Answer <> Understand

    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...
  21. N

    MHB Help with system of equations: using profits

    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...
  22. M

    Linear system of equations with parameters

    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...
  23. L

    Fortran Solving a system of equations with numeric variables - Fortran

    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...
  24. Y

    MHB A challenging system of equations

    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\\...
  25. C

    Linear Algebra solution to a system of equations

    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...
  26. E

    System of Equations: Unique Solution Conditions

    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...
  27. I

    MHB Solve System of Equations: X^2+y^2 and (x+3)^2+(y-3)^2=9

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

    How to use matrix method on this system of equations

    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...
  29. U

    Finding a Solution for a System of Equations with Trigonometric Functions

    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...
  30. anemone

    MHB Solve System of Equations: x, y, z

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

    Solving a system of equations .

    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...
  32. D

    MHB Question on solving system of equations with constants....

    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...
  33. Albert1

    MHB Solving a System of Equations in N to Find a,b,c

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

    MHB Calculating Real $(x,y,z)$ with System of Equations

    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...
  35. H

    System of equations with 2 parameters

    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...
  36. H

    Need help with basic system of equations with two unknown values

    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...
  37. N

    Is this a linear system of equations?

    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 &...
  38. A

    Linear system of equations for a differential equation

    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...
  39. M

    Linear Algebra: Solving a system of equations for damped oscillation

    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...
  40. 7

    Solving a Difficult System of Equations in Dynamics

    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...
  41. A

    Solving system of equations to find angle and energy of Au atom and α

    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...
  42. anemone

    MHB Problem Involving a System of Equations

    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...
  43. anemone

    MHB Can This Unique Pair of Values Solve the Equation?

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

    How can I solve overdetermined systems of equations using GSL?

    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...
  45. C

    Challenging System of Equations (4 Variables)

    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...
  46. S

    How Do You Derive a = mg / (M + m) from the Given Equations?

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

    Solving a System of Equations: Understanding F_B

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

    MHB Maria's problem from Facebook (system of equations)

    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
  49. P

    General solution of a system of equations and partial fractions

    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...
  50. 1

    Dealing with a nonlinear system of equations.

    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...
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