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. E

    How to Determine Values for a and b in a 3x4 System for Infinite Solutions?

    [Solved] 3x4 system of equations Homework Statement Consider the following system of three equations in x, y and z. 2x + 4y + 5z = 17 4x + ay + 3z = b 8x + 7y + 13z = 40 Give values for a and b in the second equation that make this system consistent, but with an infinite set...
  2. N

    Solve System of Eqs: Miles, Time, Boat, Current

    [SOLVED] System of equations 1. Homework Statement Use a system of equations to solve the following problems: (a.) A boat took 1 hour 50 minutes to go 55 miles downstream and 3 hours 40 minutes to return. Find the rate of the current. (b.) A boat travels 60 miles downstream in the...
  3. S

    Is a system of equations consistent?

    Homework Statement Tell if the given system is consistent or not: X_{1} -2X_{4} = -3 2X_{2}+2X_{3} = 0 X_{3}+3X_{4} = 1 -2X_{1}+3X_{2}+2X_{3}+X_{4} = 5 Homework Equations Once put into Reduced Row Echelon Form, the system becomes: X_{1}-2X_{4} = -3 X_{2}-3X_{4} = -1 X_{3}+3X_{4} = 1The Attempt...
  4. S

    MATLAB Solving a System of Equations with MATLAB

    i have two equations and 2 unknowns. i have to represent this system of equations in a matrix form and then solve it...how do i do that on matlab?
  5. R

    Efficiently Solving a Complex System of Equations in Chemical Engineering

    Homework Statement qa+2qb=10.158 4qa+6qb=200d 2qa+(7/2)qb=c 2qa+3qb=100d 3.76qc+100d=89.842 Solve for a,b,c,d,q Homework Equations The Attempt at a Solution I desperately want to avoid solving this system of equations by hand. This if for a chemical engineering class and...
  6. V

    Solving a System of Equations for Internal Forces at E

    Homework Statement The question is asking for the internal forces at E, but I get stuck solving the external reactions. After that, I can do it, and have, using electronically generated results. I just get stuck solving the system of equations I get after doing the determinant equations...
  7. M

    Finding Real Solutions: Solving a System of Equations with Inequalities

    Homework Statement conssider the system of equations a + b = 2m^2 b+c=6m a+c =2 Determine all real values of m for whcih a<=b<=c Homework Equations The Attempt at a Solution tried subtracting the equations got a-c = -4m a= -6m +2 i have no idea what I am trying...
  8. J

    Solving a linear system of equations

    Span of vectors in R3 Homework Statement u1 = (1,0,-1) u2 = (1,1,1) u3 = (3,1,-1) Determine whether the vectors span R^3. Homework Equations The Attempt at a Solution I know how to determine if the vectors span R^3(or maybe i dont). In this case checking if I can find a linear...
  9. B

    Some kind of system of equations with double integrals

    Hey there, this is my first post, hopefully I don't screw anything up. Homework Statement Suppose that ∫ ∫D f(x, y) dA = 4 where D is the disk x2 +y2 ≤ 16. Now suppose E is the disk x2 + y2 ≤ 144 and g(x,y) = 3 f( [x/3], [y/3] ). What is the value of ∫ ∫E g(x, y) dA?Homework Equations The...
  10. V

    Proving the Uniqueness of a System of Equations

    Here's a problem from one of the last (or previous of last) year, which bothers me ssssssoooooooo much. I've been working on this like a day or so, and haven't progressed very far. So, I'd be very glad if someone can give me a push on this. \left\{ \begin{array}{ccc} e ^ x - e ^ y & = & \ln(1 +...
  11. D

    What are the steps for graphically solving a system of equations?

    Homework Statement Solve the system of equations graphically. Homework Equations 1) 4x - y = 5 y = 4 - 5x^2 2) 2x^2 + y^2 = 33 x^2 - y^2 = 12 The Attempt at a Solution The answers I got for the intersecting points are: 1) (1, -1) And 2) (+/- 3.7, +/- 1.8)...
  12. V

    Solve 2 unknowns x & y in System of Equations

    Hi, I just came across this problem some days ago, and I am tearing all my hair to solve it. :cry: :cry: :cry: I am nearly bald now... :cry: :cry: The problem asks to solve for 2 unknowns x, and y: \left\{ \begin{array}{ccc} x ^ 2 + y ^ 2 & = & 1 \\ x ^ {2006} + y ^ {2006} & = & 1 \end{array}...
  13. D

    How to Solve a System of Equations with a Parabola and Ellipse?

    Homework Statement y = 5x^2 + 1 x^2 + 6y2 = 21 Homework Equations quadratic formula The Attempt at a Solution I am not quite sure how to solve algebraically... My parabola is this x|y 0 1 1 6 ellipse x|y 0 | 1.87 4.5 | 0 How can I manipulate the formula to solve...
  14. murshid_islam

    Solving System of Equations: Guidance for Australian Math Olympiad Problem

    can anyone tell me how to solve the system of equations: (x-1)(y^2+6) = y(x^2+1) (y-1)(x^2+6) = x(y^2+1) note: this is not a homework problem. as far as i know, this is a problem from australia's national math olympiad.
  15. T

    System of equations (let me see You)

    Consider the following system of algebraic equations: 2x+2y+2z-3=0 x^3+3yz^2-u=0 y^3+3x^2z-u=0 z^3+3xy^2-u=0 Problem questions: a)Is the quadruple (1/2,1/2,1/2,1/2) the only solution to the system in \mathbb{R}_{+} ? b)If the answer to a) is "yes" how to proove that fact;if the...
  16. I

    Fixed-Point Iteration for Nonlinear System of Equations

    Hello: I am solving for the fixed point of this nonlinear system: x^2 - x + 2y^2 + yz - 10 = 0 5x - 6y + z = 0 -x^2 - y^2 + z = 0 Somehow, I got stuck with my function for g, g(x) = x. I ran this in a program applying the Newton's method and I got its...
  17. P

    Do I use a system of equations for this projectile motion?

    1. Chuck Norris kicks a basketball from the ground into a basketball hoop, it makes it in perfectly. THe hoop is 150m away, and 6m above the ground. He kicks the ball at a 39 degree angle. How long does it take for the ball to reach the net? What was the initial velocity? 2...
  18. H

    Transforming Equations into Systems

    Could someone give a brief run down of how to transform a given equation into a system of first order equations. Example: u"+.5u'+2u=0 How do you transform a given system of equations into a single equation of second order. Example: x1'=3x1-2x2 , x2'=2x1-2x2 Thanks a bunch, because my...
  19. F

    Solving System of Equations: What Gives?

    I'm not sure if this even belongs in the calculus forum because it is rather basic, but here it goes. I'm working on this circuit problem and I could NOT figure out what I was doing wrong. My solution has led me to the following system of equations: (1) (2+j2)\bar I_1 +(j1)\bar I_2 = 10 (2)...
  20. T

    System of equations difficulty

    -44x^2 -2y^2 - 47xy + 45x + 2y + z =0 ; -2x^2 + y^2 + 43 xy + 2x + z =0; x^2 - 44y^2 - 41xy - 2x + 43y + z =-1 _____________________________________ :rolleyes: Can we obtain all REAL solutions of this system without using numerical math tools? I have problems with it and would...
  21. E

    Solving System of Equations for t and b

    How would you solve the following system of simultaneous equations for t and b? sin(pi*t) = 0 sin(pi*(t^2 + 35)/(2*t)) = 0 (t^2 + 35)/(2*t) - t/2 - b/2 = 0 t^2/35 +35/t^2 -t/b - b/t = 0 t*b = 35 inquisitively, Edwin G. Schasteen
  22. D

    Solving a System of Equations Without a Calculator

    Hi, this should be the last question for today :lol: Determine the number of solutions for the following system: y = -4log_{12} (x) y = 4 sin(x) Is there a way to do this without using a graphing calculator? Thank you very much!
  23. B

    Chemistry and system of equations

    Hi, I want to kow if it is possible to convert a chemical equation ( unbalanced) into a matrix and solve this matrix to find the coeficient of the equations to balance the equations. For example: H2SO4+MnS+As2(Cr2O7)5---->HMnO4+AsH3+Cr2(SO4)3+H2O How to convert it into a matrix of unknowns...
  24. F

    MATLAB Plotting System of Equations in MATLAB

    Maybe not the proper place to post... but it seems like physics forums is going through some type of "crazy" change right now. Anyways... I'm having trouble finding a website with directions on how to plot a system of equations in MATLAB. If anyone has a basic M-file they could show me, or a...
  25. E

    Solving a System of Equations with Matrices

    Hi, I've just been given a set of revision questions for matrices and I'm having problems with the following question: http://tinypic.com/ejbssz.jpg" My task is to find the general solution of this system (if there is any). Do I start off by reducing it to row echelon form and then...
  26. P

    System of Equations Mechanics problem

    The x-coordinates of two objects moving along the x-axis are given below as a function of time t. x_1 and x_2 never have the same value. Calculate the value of x_2 when the objects are nearest to each other. x_1= 23.0t x_2= -28.0 +43.0t-8.0t^2 I solved the first equation for t, and...
  27. J

    MATLAB Solving Nonlinear System of Equations for x and y as a Function of r

    1. a line in my code is something like int(phi*x^2,0,2) where i want phi to be a function which the user has choosen. But how can i let the user choose a function? For numbers you can use input but how to do it with a function? 2. i want to solve a nonlinear system of equations...
  28. S

    Is the System of Equations Inconsistent Despite a Solved Example?

    0a - 2b + 3c = 1 3a + 6b - 3c = -2 6a + 6b + 3c = 5 I got a = 3, b = 3/2, c = -4/3 but the book says that this system is inconsistent. It asks us to use Gauss-Jordan elimination (which I have used on the past 5 or so problems and got all the right answers). I know how to do these, I just...
  29. C

    Solving Systems of Equations: Definitions and Examples

    Hi everybody, Here are some definitions that I want you to comment/correct: 1)Equation: An equality that contains variables. The values of the variables(or if we talk about real numbers, the numbers) that make the equality "true" are called solutions of the equation. So when we say "solve...
  30. L

    Solving a System of Equations with Matrix

    Hi! I'm trying to solve an equation system \vec{\pi}\mathbb{P} = \vec{\pi} where \vec{\pi} = (\pi_1, \pi_2, \pi_3, \pi_4, \pi_5) and \mathbb{P} is a 5x5 matrix (constants). The problem is that the equation system is a bit to large to handle, at least for me. I remember that linear equation...
  31. R

    Is the Matrix A with Entries aij=min(i,j) Always Invertible?

    Help! System of equations! For a natural number define the n*n matrix A = (aij) by setting aij = min(i,j). Write down the matrix a for a few values of n = 2,3,4... Show that A is invertible and find its inverse. Hence or otherwise show that the system of equations Ax =b , where x=(x1,...xn)...
  32. N

    Creating a system of equations

    I would like to thank-you for taking the time to read the current problem that I am going through. I understand the system of equations concept well however in this particular question they ask for me to produce a system of equations from a certain situation and then solve it myself. Here is the...
  33. S

    Reducing a System of Equations to One Variable

    Hello, I am difficulty solving this system of equations. Eqn1: 1.0416*10-21 = 4.75*10-27(x2) + 1.68*10-27(x1)(cos a) Eqn2: 2.827 = (x1)(sin a) Eqn3: 3.22896*10-16 = 8.4*10-28(x2)2 + 3.36*10-27(x1)2 I keep on getting equations with two variables in it. Can someone tell me how to...
  34. D

    Solving a System of Equations: What Gives?

    This seems like a very simple problem, yet I can't seem to come up with the correct solution. Determine all the values of c for which the system has nontrivial solutions, and then find all the solutions. x + 2y + cz = 0 3x - y = 0 -2x + y + z = 0 OK, the system has...
  35. zeronem

    What Are Common Errors When Solving Complex Systems of Equations?

    I found this System of Equations to be a real pain, I've come up with a lot various answers and some of them have worked, but then when i try it on others, they don't work. x + 2y = 5 3x +4z = 2 2y + 3w = -2 3z - 2w = 1 Ive tried solving this so many times. I've gotten z = 29/35, x=...
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