What is Simultaneous equations: Definition and 125 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. J

    Solving simultaneous equations F = ma

    Homework Statement Luke stands on a scale in an elevator which has a constant acceleration upward. The scale reads 0.97 kN. When Luke picks up a box of mass 20 kg, the scale reads 1.18 kN. (The acceleration remains the same.) (a) Find the acceleration of the elevator. (b) Find Luke's...
  2. P

    MHB Why Does the Same y Value Satisfy Both Equations in Simultaneous Equations?

    consider the equations which we want to solve simultaneoulsy: 2x+y =10 (*) 3x+4y=25 (**) By peforming 4(*) - (**), we have 5x =15 i.e. x=3. Now my question is this: Why does the same y value (y=4) satisfy both original equations? This always happens. We never find that, having found x...
  3. W

    MHB Four Non-Linear Simultaneous Equations

    4 equations, 4 unknowns: \[\frac{u(r^2 - u^2)}{r^2 + u^2}=156~~~~~~~~~~(1)\] \[\frac{v(r^2 - v^2)}{r^2 + v^2} = 96~~~~~~~~~(2)\] \[\frac{w(r^2 - w^2)}{r^2 + w^2} = 63~~~~~~~~~~(3)\] \[\frac{315uvw + 24336vw + 9216uw + 3969uv}{2r} = 943488~~~~~~~~~(4)\] Who can solve that mess?
  4. A

    Simultaneous Equations: Solving for θ with FA and NA

    Homework Statement I have two eqs. but am stuck on solving them.Homework Equations FA - 10sinθ = 0 NA - 10cosθ = 0 Where FA = 0.15NA The Attempt at a Solution I've substituted the 0.15NA into the first equation but am still not sure how to get θ? I'm sure its something easy that I'm just...
  5. C

    MHB Solve Simultaneous Equations: Find X & Y Values

    I have been trying to find the values of x and y for these simultaineous equations by the method of substitution, but I can only get so far before I become confused what to do next? 2x + 3y = 5 5x - 2y = - 16 I worked out; y = 1/3(5 - 2x) and combined them y = 5x - 2/3(5 - 2x) = - 16 then I...
  6. FeDeX_LaTeX

    Can You Find the Unique Solution to These Simultaneous Equations?

    The problem: "xy + yz + zx = 12 xyz = 2 + x + y + z Find a solution of the above simultaneous equations, in which all of x, y and z are positive, and prove that it is the only such solution. Show that a solution exists in which x, y and z are real and distinct." I haven't really made much...
  7. C

    MHB Simultaneous equations in word form (2)

    The wage bill for six women and five men is \$670. The bill for eight men and three women is \$610. Find the wages of (1) a man and (b) a woman. i set it up like this : 6x+5y=670 3x+8y=610 did i set it up right because word questions confuses me .
  8. C

    MHB Simultaneous equations in word form

    Two numbers are such that 5 times the first is three more than 6 times more than the second. Four times the second is five more than the first. Find the numbers. and also The sum of two nubers is 90. If 20 is added to 3 times the smaller number, the result exceeds twice the larger by 50. Find...
  9. Y

    Help with applying the least squares method for solving simultaneous equations

    Hi everyone given the system of equations A1Cx + B1Cy + C1Cz = D1 A2Cx + B2Cy + C2Cz = D2 A3Cx + B3Cy + C3Cz = D3 I need to solve for Cx, Cy, Cz All other variables are known and constants. However all other variables (A,b,c,d) come from experimentally measured data and thus I cannot...
  10. N

    Solving Simultaneous Equations

    I need help solving these two equations simultaneously y = c_1e^{r_1t_o}+c_2e^{r_2t_o} y' = c_1r_1e^{r_1t_o}+c_2r_2e^{r_2t_o} My plan of solving these two equations is by substitution. By rearranging I obtain the following: c_1 = [y-c_2e^{r_2t_o}]e^{-r_1t_o} c_1= \frac{[y'...
  11. K

    Simultaneous equations with 3 Unknowns

    Help chaps I am having a bad time with this. I can appreciate this is basic, however i can not get my head around it. Im scrubbing up on my maths as i was thinking of doing a HND in Engineering. I am working my way through K.A. Stroud's Engineering Mathematics and simply can't get to grips...
  12. J

    Solving Simultaneous Equations with 2xy: Tips and Methods

    I have the following simultaneous equations. However I am unsure how to handle that 2xy. Can someone give a pointer to any known methods? x= 3x^2+2xy y=x^2+3y+8
  13. T

    Explanation for Simultaneous Equations Solution

    Hi, there's this simultaneous equation problem, however I already know the solution, I just want to know more about the solution. a+b+c=2,bc+ac+ab=-5, abc=-6 The solution is: Consider the polynomial (x-a)(x-b)(x-c), where a,b,c are constants. (x-a)(x-b)(x-c) = x^3-(a+b+c)x^2+(bc+ac+ab)x-abc...
  14. M

    How Do You Solve Simultaneous Equations Using Quadratic Methods?

    Homework Statement How do yo solve simultaneos equations? Homework Equations Am I right ? The Attempt at a Solution y = x2 – 5x + 5 question a 5x + 3y = 30. question b Find location of points collide? Add a+b x2 + 2y -25=0...
  15. A

    Solving rectangular form simultaneous equations?

    Hi, I have the following 3 simultaneous equations to solve for the currents I1, I2 and I3: I1(0-j5) + I1(5+j5) - I3(5+j5) - 20 = 0 I2(5+j5) + I2(0-j10) + I3(0-j10) - 20 = 0 I1(0-j5) + I3(10+j0) - I2(5+j5) = 0 Does anyone have the link to any online software I could use to solve the...
  16. R

    Best method to solve simultaneous equations?

    I am learning about solving simultaneous equations with matrices but they make less sense to me and take more time than solving the equation using the method rearranging the formulae so that you can eliminate the other variables and then repeat for the other variables? I'm thinking of giving...
  17. H

    Solving Simultaneous Equations: x^2 + y^2 = 10 and y = 2x - 5

    Homework Statement Sure I could do this by looking at the mark scheme, but i need to know HOW and WHY, so that in the future i can do these equations by myself. Thanks :) by elimenating y, solve the simeltaneous equation Homework Equations x^2 + y^2 = 10 y = 2x - 5 The Attempt...
  18. R

    Solving Simultaneous Equations with Positive Numbers

    Homework Statement 2 positive numbers , x and y, are such that the sum of their squares is 10 times their sum. a. write an equation to link x and y b. If y is the larger number and the difference is 6 show that x satisfies the equation x2-4x-12=0 c. solve the equation and fin the 2...
  19. K

    Solving a Problem with 4 Simultaneous Equations and 6 Unknown Variables

    I have a problem that involves 4 simulationious equations with 6 unknown variables. Been trying to solve it using elimination but getting stuck in a loop. Any advice on how to solve this? I know there will be multiple answers. Is elimination the best method? Can't upload the problem now...
  20. L

    Problem doing force analysis using simultaneous equations

    hi guys ive got a problem whils solving a force analysis on a crane truss, when i get to a joint where simultaneous equations are needed. have a look at what I've got and itll make more sense. when i equate the two equations they don't balance. from my previous working i get F2=9810...
  21. J

    How can I solve a simultaneous equation with unknown angles in it?

    Hey guys, I am currently studying Engineering, and its only my first year. I am having trouble with one of the simultaneous equations i have made from a physics question. I don't know how to solve this because the uknowns are both angles. I have attached a photo of the simultaneous equation...
  22. K

    Question on force and simultaneous equations

    Homework Statement Question: If an 80kg object experiences a normal force of 510N, and an unknown angled pull force. The coefficient of friction is 0.33. If the object moves with a constant velocity, what is the direction (angle) and magnitude (size) of the pull force? m=80kg a=0m/s...
  23. O

    Solving 3 variables - simultaneous equations

    hi, my sister came to me with this problem today, and i was stumped to believe this is 'year 8/9' work, but nevertheless, could you please provide me with a path, been trying to solve this for her for ages! Homework Statement p = $1.60 each, p = 40c each and a = 70c each. At the shop...
  24. K

    Mathematica Solving simultaneous equations with big matrices using Mathematica 7

    Hi all, Please help me to solve my problem in Mathematica that involves simultaneous equations with large matrices. The code is provided in the attached file, Exercise1.nb the errors say like this " General::unfl: Underflow occurred in computation. >> General::unfl: Underflow occurred...
  25. J

    How Do You Solve Simultaneous Equations for Revision?

    Homework Statement Question is in the attachment, this is for revision not homework
  26. A

    Using the theory of simultaneous equations

    Homework Statement A, B, C and D are celebrating their joint birthdays and find that their ages add up to exactly 100 years. The sum of A's and D's ages equals the sum of B and C, while the di fference between the ages of A and D is twice C's age. Finally when D is as old as A is now, C...
  27. L

    Solving simultaneous equations

    when solving a system of simultaneous equations in matrix from (with the LHS = 0) why does the determinant of the matrix need to vanish? thanks
  28. M

    Solving Simultaneous Equations

    Homework Statement I need to solve these two equations to obtain expressions for X(t) and Y(t) Homework Equations [1]. \frac{d(X(t))}{dt} = Q \cdot Y(t) [2]. \frac{d(Y(t))}{dt} = -Q \cdot X(t) The Attempt at a Solution Perhaps rearrange equation [1] to get in terms of Y(t)...
  29. J

    Differential equations- simultaneous equations

    Homework Statement http://img228.imageshack.us/i/cimg5162f.jpg/ This isn't the usual format, so I hope it's still ok. It's just easier than writing it out on here. I can't work out how to form a simultaneous equation from (1) and (2). When solved it should form the du/dx and dv/dx...
  30. 0

    Simultaneous Equations From Kirchhoff's Rules

    Homework Statement For a Lab report I have to solve for three unknown currents from Kirchoff's Rules equations using simultaneous equation algebra, and I'm completely stumped.Homework Equations From Loop and junction equations, the three equations that I have are I1 + I2 = I3 I1= (-I3R3 -...
  31. R

    Solve Simultaneous Equations to Find OP: a & c Given

    Ok, I'm new here, and I'm not sure if this is the right place to ask. So anyway here's the question: OABC is a square. M is the mid-point of OA, and Q divides BC in the ratio 1:3. AP and MQ meet at P. If OA=a and OC=c, express OP in terms of a and c. The question's easy enough... until the...
  32. T

    Solving Simultaneous equations using Matrices

    I have to teach myself pre-calculus and basic calculus over the summer, and whilst covering matrices the chapter on solving simultaneous systems of equations using matrices puts forth several methods, one of which being the method of Gaussian elimination with augmented matrices. I understand why...
  33. O

    Further Maths (Matrices and solving simultaneous equations)

    Homework Statement FP1 (MEI June 07) Homework Equations The Attempt at a Solution (i) Find the value of n I multiplied the top row of A by the left column of B and got the equation: -5-16+k=k-n moved stuff around and ended up with n=21 (ii)Write down the inverse matrix A-1...
  34. F

    Need help solving these simultaneous equations, anyone with a pen and paper?

    Solve -r*(T^2 + T + 6) + 1 = 0 4r*(T^2 + T) - T = 0 For T and r One solution is T=0 and r=1/6 There are 2 more. I have T = +- i/(2)0.5 and r = 1/[4(1+T)] But MATLAB is disagreeing with my solutions, can anyone rectify them for me please?
  35. K

    Simultaneous equations are missing some solutions

    Hey everyone! Homework Statement This is part of a question on finding minima,maxima and saddle points in multi variable functions. In this section i need to solve the differential equations: y^{3}+3x^{2}y-y [1] x^{3}+3y^{2}x-x [2] Homework Equations --- The Attempt at a...
  36. W

    Simultaneous equations using exponential functions

    Homework Statement Solve the following equations using simultaneous equations Homework Equations 32x\times23y=17 4x\times5y=37 Appologies for the bad equation set-up. The large 'x' is a multiplication sign. The Attempt at a Solution My attempt was to divide both of the...
  37. T

    Quadratic & simultaneous equations

    Homework Statement A sprinter accelerates from rest to a top speed with an acceleration which magnitude is 3.80 m/s^2 . After achieving top speed, he runs the remainder of the race without speeding up or slowing down. The total race is 50 m long. If the total race is run in 7.88 s, how far...
  38. C

    Questions on 3 simultaneous equations (3D vector planes)

    Homework Statement 1) Determine, by elimination, value of a (if any) such that the given system will have a unique solution x+2y+3z=2, 2x+2y+az=0, 3x+2y+z=0 2) Determine, by elimination, values of a (if any) such that the given system: a) Is consistent with and infinity of...
  39. B

    Hope this helps!Solving Simultaneous Equations with Square Roots

    Hi How do you solve this equations analyticaly without solving a 4th degree polynomial sqrt(x)+y=11; x+sqrt(y)=7 Thanks
  40. Mentallic

    Simpler Approach for Solving Simultaneous Equations with Multiple Variables?

    I need to solve these 2 equations: r^2-a^2=\sqrt{(r^2-a^2)(R^2-(b-d)^2)} \sqrt{(r^2-a^2)(R^2-(d-b)^2)}=R^2-d^2+bd-ab+ad Now wait, before you run off thinking "screw that - too many letters, too much hassle" I don't actually want you to solve this for me, but I have a question about it...
  41. R

    Solving for variables using 3 different equations (simultaneous equations)

    Homework Statement Solve for A, T1 and T2. Equa 1) T1 + 25.0a = 245 Equa 2) T2 − 10.0a = 98.0 Equa 3) T1 − T2 − 80.0a = 78.4 Homework Equations As above. The Attempt at a Solution I isolated a in the first equation: a = (245-T1)/25 and T2 in the second equation: T2...
  42. V

    Simultaneous Equations check on work

    Guys I have an assigment to hand in I am back at college again. Mature student so as this might be simple for some it sometimes is not for me(out of school 10 years) I have uploaded 3 pages, questions 1,2,3 I have completed. but I just need to have them checked to see if they are correct. And...
  43. C

    Simultaneous Equations Homework Statement: Solving with Two Variables

    Homework Statement Eq 1: (4.5 - V1)/470 = V1/680 + (V1-V2)/330 Eq 2: (V1-V2)/330 = V2/100 + (V2+7)/1000
  44. C

    Finding W and Theta in Simultaneous Equations

    Homework Statement 160 cos(theta) - W cos(69) = 0 160 sin(theta) - W cos(21) - W = 0 Can someone solve these equations for me to find W and theta?
  45. M

    Least squares solution to simultaneous equations

    I am trying to fit a transformation from one set of coordiantes to another. x' = R + Px + Qy y' = S - Qx + Py Where P,Q,R,S are constants, P = scale*cos(rotation). Q=scale*sin(rotation) There is a well known 'by hand' formula for fitting P,Q,R,S to a set of corresponding points. But I...
  46. S

    Solving Simultaneous Equations: Step-by-Step Guide and Explanation

    Homework Statement Find a,b,c,z 2a+b+2c=z a+2b+c=4 a+b+2c=3 2. The attempt at a solution Ok so I've tried multiplying all lines by 2 so you may possibly cancel out 2a, but not sure where to go after i multiplied everything. Then i tried to just cancel one equation and then another...
  47. T

    Methods for solving simultaneous equations

    Hey everyone. Okay, first of all I'm not sure if these equations are simultaneous or linear so please correct me if I'm wrong. I need to know a simple procedure to tackle on these equations.Thanks. a) y=x-6 and y=2x-14 b) y=0.5x-7 and y=3x-22 c) 9y-4x+6=0 and 4x-2y-7=0
  48. M

    Simultaneous equations with an integral

    Hello I am having a problem solving a set of simultaneous equations in mathematica. One of the equations is an integral, with the unkowns as limits of integration, and the other is a function containing both variables, but no closed form solution can be found for either variable. I am...
  49. P

    Can Simultaneous Equations Have Multiple Solutions?

    please help me (Simultaneous Equations) 4x+3x=28 2x+5x=42 how can i sole it from gaussian method :(
  50. Mentallic

    Is it possible to find a lower degree polynomial for sqrt(4+sqrt(2)+sqrt(6))?

    I have had quite a bit of experience solving simultaneous equations from high school (haven't learned matrices) by various - but mostly - rearranging one variable and substituting it into another equation, but recently I was attempting to remove a surd upon another surd (lack of a better word)...
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