What is System of equations: Definition and 282 Discussions

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. B

    Solve this System of Equations: .5= (x-40)/(x-y) and .5=(40-y)/(x-y)

    Homework Statement Solve for x and y .5= (x-40)/(x-y) and .5=(40-y)/(x-y) Homework Equations The Attempt at a Solution I have been trying to solve this system of equations for hours and I can't seem to get it. Can anyone please give it a shot and see what they get? I'm sure I...
  2. B

    Not sure how to solve this system of equations (easy)

    Homework Statement Im trying to find local min and max values. So I have fx and fy. I need to find critical points by setting them equal to 0 4x^3-4y=0 and 4y^3-4x=0 Homework Equations 4x^3-4y=0 and 4y^3-4x=0 are fx and fy respectively The Attempt at a Solution I...
  3. L

    Missing Components and 3D Vector Resolution by System of Equations

    1. Hi I am writing a program to calculate 3D vectors for visualization and I am testing textbook problems such as: "If vector c forms an obtuse angle with the 0Y-axis and is orthogonal to both vectors a = 3i + 2j + 2k and b = 18i - 22j - 5k Find the components of c if its norm...
  4. A

    System of Equations: Find m, Graphical Interpretation

    Homework Statement Shown in the figure is the graph of x = y^2 and a line of slope m that passes through the point (4, 2). Find the value of m such that the line intersects the graph only at (4, 2) and interpret graphically.Homework Equations x = y^2 y = mx + bThe Attempt at a Solution Since...
  5. F

    System of equations using modulo

    Homework Statement 5) Determine the inverse of the matrix \begin{bmatrix} 6 & 17\\ 13 & 21 \end{bmatrix} mod 26 Homework Equations Solve for linear system of equations: 6a + 17c = 1 mod 26 6b + 17d = 0 mod 26 13a + 21c = 0 mod 26 13b + 21d = 1 mod 26 The Attempt at a...
  6. L

    A system of equations with more unknowns than equations

    Hello, It is known that a system of linear equations is considered overdetermined if there are more equations than unknowns... My question simply stated: is there a term to describe a system of linear equations if there are more equations than unknowns? Google seems to struggle when my...
  7. A

    Solving trigonometric system of equations

    Hi. I'd like to know whether is it possible to do the following, and if so, how...(and also, whether is it possible to solve similar problems) I have parametric equation of a curve and I need to find its intersection with a ray that starts at the origin of the coordinate system and makes...
  8. L

    Relation of a Matrix and a System of Equations Question

    Hello, I just have a general question regarding if my analysis of the relationship of system of equations and the matrices constructed involved in solving them. If systems of equations can be solved through matrices (Vandemonde...etc) by obtaining the inverse of the coefficient/variable...
  9. G

    How Do You Solve for Z in Terms of X and Y?

    Well, okay. I have this system of equations, kind of. Rather than looking for a number, though, I'm looking for a function. I'll try to explain myself as best as I can, but I'm not really familiar with the terms I should probably be using. Basically, x and y are on the left side of this...
  10. T

    How to Solve a System of Equations Without Using Matrices?

    Homework Statement Solve for a, b, and c. 4c+6b+14a=25 6c+14b+36a=21 14c+36b+98a=105 Homework Equations The Attempt at a Solution I need to solve this without using matrices. The easiest way would be to get it into row echelon form and back-substitute. However, I'm not sure how you can...
  11. F

    Complex Thermo-Dynamic System of Equations

    I took AP Physics (failed) back in high-school, and I've retained most of the information, but we didn't delve too far into thermo-dynamics, instead focusing mostly on resistance, acceleration, velocity, friction, ect... I am trying to calculate a few things to determine the average...
  12. E

    System of Equations and Inequalities

    Homework Statement Solve each sysytem usiing any method you wish: x2-y2=21 x+y=7 Homework Equations x2-y2=21 x+y=7 The Attempt at a Solution I chose to do the substitution method. so i change equation 2 to this: y=7-x and substitute it into the other equation in place...
  13. E

    Proving a System of Equations: 3xy+y^2=-7 and x^2-2xy=30

    Homework Statement How do we prove the system of the following equations?? 1) 3xy+y^2 =-7 2) x^2-2xy = 30 Homework Equations The Attempt at a Solution I tried by solving the 1st equation in terms y and then substituting into equation (2) but the problem got more...
  14. M

    Solving Linear System of Equations with Discrete Components

    Hi community, I have a linear systems of equations (8x8), but the matriz's components are discrete. In this moment, I make values' all of components and I write them in 64 files of 150x6000. My question is How do you solve a linear systems of equations discrete?, I mean, How do I work with...
  15. I

    MATLAB MATLAB: system of equations (HELP)

    Hi to all. I have to say at first that i have no idea on MATLAB at all. I want some help. I want to solve a system of equation for example (0.02315352 - 0.0576` Cos[\[Theta]] + 0.01152 Cos[\[Theta]]^3) Cos[\[Phi]] - 0.01152 Cos[\[Theta]] Cos[\[Phi]]^3 Sin[\[Theta]]^2 - 0.001919...
  16. M

    Write down the linear of system of equations

    Homework Statement write down the linear system of equations that must be satisfied to find the Newton-Cotes quadratic rule for the interval [0,1] that is exact for polynomials of degree 3 and uses the sample points x1=0, x2=1/3, x3=2/3, and x4= 1 Homework Equations none The...
  17. L

    Variation of Parameters, system of equations

    Homework Statement y''+25y=cot(5x) Find one possible solution The Attempt at a Solution I don't have any background in linear algebra, so I can't use cramers rule as a heads up, so I have to solve the system of equations (no linear algebra for this course is needed). Ok, so I take...
  18. L

    Algebra 1b - System of equations

    Homework Statement The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number ------------ I Don't understand when they say the digits are reversed, i have done these problems many times before. but i don't understand the...
  19. S

    Differential Equations: System of equations

    Homework Statement I have the following 2 equations dx/dt = 3x+y and dy/dt = sqrt(y) I need to find the general solution to the system. Homework Equations dx/dt = 3x+y and dy/dt = sqrt(y) The Attempt at a Solution i did the y equation first using separation of variables and got...
  20. R

    Uniqueness of a system of equations

    Homework Statement Its number four on this link: http://www.math.pitt.edu/~dwang/math0280/math0280-r1.pdf" The Attempt at a Solution Well I reduced it to echelon form, and that's not really what I have the question on. But I have three equations now, but I am not sure what values of k would...
  21. T

    Arithmetic mean of two unknowns in a system of equations

    Homework Statement When finding the arithmetic mean in a system of equations is there any reason why the method that I am using is wrong? Find the arithmetic mean of x and y in the following set of equations Homework Equations 3x + 5y = 65 and 7x + 14y = 175 The Attempt at...
  22. T

    Optimization - help needed setting up a system of equations?

    Homework Statement A truck driving over a flat interstate at a constant rate of 50 mph gets 4 miles to the gallon. Fuel costs $0.89 per gallon. For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon of its mileage. Drivers get $27.50 per hour in wages, and the...
  23. T

    Nonlinear System of Equations Newton-Raphson and SOR Sucessive Over Relaxatiom

    Homework Statement 3X1 - COS(X2*X3) – 0.5 = 0 X1^2 - 81*(X2 + 0.1)^2 + SIN(X3) + 1.06 = 0 EXP(-X1*X2) + 20*X3 + (10pi – 3)/3 = 0 Homework Equations Newton Raphsom and Gauss Sceidal with relaxation term The Attempt at a Solution I've already solved the above system using Newton...
  24. D

    Newton's method for a system of equations

    Under what circumstances will Newtons method for a system of nonlinear equations converge? Are there any criteria at all which guarantees convergence? Regards
  25. C

    Help with Solving a System of Equations

    I have been trying to solve this problem for a whole week without success, I need help. Solve the following for x,y and z: 2x+5y-z = 18 7x-y+4z = 22 6x+2y-3z = 0.1x + 0.2y + 0.3z I have already combined all the terms of eq.#3 and equal it to zero, but it didn't work. I also...
  26. T

    Define coefficients for system of equations with 3 variables

    Homework Statement I have the following system og equations: \left\{\begin{array}{l} y + 2z = 1 \\ x + 4y + 3z = C \\ x + y + Bz = B \end{array}\right. a) Create the augmented matrix and reduce to row echelon form (I've already done this) b) For which values of A and B is...
  27. P

    Arithmetic Progression + System of equations + binomial

    Homework Statement A third degree polynomial has 3 roots that, when arranged in ascending order, form an arithmetic progression in which the sum of the 3 roots equal 9/5. The difference between the square of the greatest root and the smallest root is 24/5 Given that the coefficient of the...
  28. G

    Constants in a system of equations that makes the system consistent

    Homework Statement The Attempt at a Solution For a) I just solved simultaneous equations, a link to a resource that solves a system more efficiently would be nice but augmented matrices are taught in the syllabus, or atleast not in the official text. Although I've seen solutions in...
  29. U

    Solve system of equations with inverse matrix

    Homework Statement Find the inverse matrix of A, then use this inverse to solve system of equation. A is a given 3 x 3 matrix and the system of equations is 3 equations in 3 unknowns. Homework Equations The Attempt at a Solution I have found the inverse of A using an...
  30. J

    Solve System of Equations: tx'=x+y, ty'=-3x+5y

    Homework Statement solve for x and y: tx' = x + y ty' = -3x + 5y Homework Equations The Attempt at a Solution normally if the t was not in front of the primes then i'd set it up as: (D-1)x -y = 0 (D+3)x -5y=0 but I am not sure what to do when the variable t is there...
  31. A

    Maple Maple, plot system of equations, matrix.

    Hello, I have scavenged the internet and have not been able to figure out how to plot a series of equations in matrix form using maple. for example y = [a,b,c] * x + [4,5,6] would be y1 = a*x + 4 y2 = b*x + 5 y3 = c*x + 6 plot (y1,y2,y3 versus x). I have attached my actual...
  32. S

    System of equations 4 variable

    Homework Statement Solve 2w + 2x - 5y + z = -16 (1) -w + x + 6y - z = 15 (2) 2w - x + y + 6z = 3 (3) w + x + 2y - z = 7 (4) The Attempt at a Solution (2) + (4) = 2x + 8y - 2z = 22 (5) 2(2) + (3)= x + 13y + 4z = 33(6) 2(2) + (1)= 4x + 7y - z = 14 (7) --------------------------------------...
  33. J

    Program to solve system of equations

    I need a easy-to-use (i.e. no programming, if possible) program that's free that can solve a system of equations with 6 variables and 6 equations. Any suggestions?
  34. K

    Solving System of Equations: Partial Fraction Decomposition Help

    Hello. I'm trying to solve a system of equations problem (for my Partial Fraction Decomposition problem)... 1 = -4 + 2B + 2C + D + E 3 = 4 - 2B + 2C - D + E 3 = -25 + 20B + 10C + 4D + 2E 5 = 25 - 20B + 10C - 4D + 2E So that boils down to.. 1 = 2C + E 3 = 2C + E 3 = 10C + 2E 5 =...
  35. T

    Minimizing error function -> sloving linear system of equations

    Homework Statement I want to find certain coefficients \alpha_{uv} by minimizing a error function. In the end, I want to make a function of this, so iteration is not a problem. I want to estimate these coefficients to find the best estimate for f(x,y). Homework Equations The error...
  36. D

    How to express solution to system of equations

    Sorry if this is too basic for this forum, but it IS from a 2nd-year linear algebra course. I'm probably just being stupid, and missing something obvious, but here goes: Homework Statement Solve the following system of equations: 2x_{1} - 2x_{2} - 3x_{3} = -2 3x_{1} - 3x_{2} - 2x_{3} +...
  37. fluidistic

    Condition of a system of equations to have infinitly many solutions

    0. Homework Statement For which values of "a" the following system of equations has a unique solution? Infinitly many solutions? x-y+z=2 ax-y+z=2 2x-2y+(2-a)z=4a 1. The attempt at a solution I've put the system of equations under an amplied matrix and I reduced it. I finally got...
  38. M

    How Do You Solve Complex Hyperbolic and Trigonometric Systems of Equations?

    Please, have a look on this weird system of equations: a*(sinh(x)-sin(x))+b*(cosh(x)-cos(x))=c*(sinh(y)+sin(y))+d*(cosh(y)+cos(y)) b*(sinh(x)+sin(x))+a*(cosh(x)-cos(x))=-d*(sinh(y)-sin(y))-c*(cosh(y)+cos(y)) a*(sinh(x)+sin(x))+b*(cosh(x)+cos(x))=c*(sinh(y)-sin(y))+d*(cosh(y)-cos(y))...
  39. Y

    Solve 6-Var System of Equations for Unknowns

    Homework Statement I have 6 equations with six unknown variables. Does anyone know the best way to proceed? I've tried to substitute but it won't work for me. 1.Ax+Bx+.03536F2=0 2.Ay+Cy-212.1+.6124F2=0 3.Bz+Cz-.7071F2-212.1=0 4.-3Bz-4Ay+(5)*212.1+(5)*212.1=0 5.4Ax+5Cz=0 6.5Ax+3Bx-5Cy=0...
  40. Y

    Really simple system of equations

    Homework Statement 1. 2500-Tac cos \Phi=0 2. Tac sin\Phi-500=0 Homework Equations The Attempt at a Solution I have 2 equations. I need to solve for \Phi to get Tac. I have got to the point of : Tac=500/sin\Phi 2500-500/sin\Phi*(cos\Phi)=0 after this i can't go any further...
  41. H

    Find all ordered pairs (x, y) that satisfy the system of equations

    1. Find all ordered pairs (x, y) that satisfy the system of equations given below: * (x + 1)^2 + |(x + 1)(y − 2)| + (y − 2)^2 = 7 * x^2 + y^2 + 2x − 4y − 5 = 0 2. If the area of a certain rectangle is 48, and the length of its diagonal is 10, find its perimeter. here's what i did...
  42. B

    MATLAB Help with Matlab: Solving System of Equations

    Help with Matlab! Hi, I've just started learning how to use the Matlab and came across this question in the textbook: Consider the following system of equations: [-1 2 4 1 0] [ 5 4 0 0 0] [ 0 6 1 0 4] x = [ 0 -1 0 -1 4] [ 1 0 -2 -5 1] [ 1 ] [ 1 ] [ 1...
  43. S

    Solution of System of Equations: [Lambda] = 3/(2x)

    [lambda]=3/(2x) = 1/(2y) = 1/(3z) with constraint eq. x^2+2y^2+6z^2=1 The Attempt at a Solution - I can't figure out how to solve this system of equations. Can somebody please help.
  44. H

    LaTeX How do I write a system of equations with dots in latex?

    Hi Folks, I want to write a system of equations in latex. The equations is something similar as follows, http://farm4.static.flickr.com/3081/2466547973_636ea6137f_o.jpg Generally, its ok to write system of equations in latex. But i don't have any idea how can I place the dots like what you...
  45. P

    System of Equations: Solving for (x,y)

    [SOLVED] System of equations problem I'm trying to brush up on my algebra and had difficulties with a problem. Solve for (x,y): (x^-(2/3))(y^(2/3)) = (2x^(1/3))(y^-(1/3)) and 6 = x + 2y I'm mainly having problems simplifying the first equation for y but got y=0. Any help?
  46. N

    How to Solve a System of Equations with Multiple Variables and Equations

    Homework Statement Well, I am in the middle of solving a (quite difficult) differential equation using the Method of Undetermined Coefficients, and have finally come across a system of equations and I need to solve for A(sub 1), or (A1), (A2), (B1), and (B2), but I cannot figure out how to...
  47. R

    Jacobi Method; Simple system of equations

    I know this is simple, and I am missing something obvious. I'm suposed to use the "jacobi method"; and with each iteration it should be getting closer and closer to the solution (x=2 and y=1, which it is not). Could someone explain what I'm doing wrong, or how to start...
  48. 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...
  49. 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...
  50. 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...
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