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. paulb203

    Solving Simultaneous Equations: 4x + 5y =12 and -8x + 4y =32

    I multiplied the top one by 4, and the bottom one by 5 to make the y coefficients the same and got; 16x + 20y = 48 -40x + 20y = 160 Then I subtracted the bottom one from the top one and got; -24 x = -112 Which gave x = 4.666... But the answer for x was -2 I realise now that if I had...
  2. chwala

    Solve the given simultaneous equations that involves hyperbolas

    My approach on this; ##\dfrac{x^2}{4}-\dfrac{y^2}{9}=\dfrac{y^2}{4}-\dfrac{x^2}{9}## ##9x^2-4y^2=9y^2-4x^2## ##13x^2-13y^2=0## ##x^2=y^2## Therefore, on substituting back into equation we shall have; ##\dfrac{x^2}{4}-\dfrac{x^2}{9}=1## ##9x^2-4x^2=36## ##5x^2=36## ##x^2=7.2##...
  3. E

    B Attempt to solve this system of three linear equations

    The point (1, 5) is on the curve: y=ax^2+bx+c. This point gives the linear equation: 5 = a + b + c. A second point on the curve, (2, 10) gives the linear equation 10=4a+2b+c. A student called Erika thinks that the point (2, 19) is also on the curve. 5 = a + b + c. 10=4a+2b+c 19=4a+2b+c the...
  4. chwala

    Solve this pair of simultaneous equations involving complex numbers

    $$(1+i)z+(2-i)w=3+4i$$ $$iz+(3+i)w=-1+5i$$ ok, multiplying the first equation by##(1-i)## and the second equation by ##i##, we get, $$2z+(1-3i)w=7+i$$ $$-z+(-1+3i)w=-5-i$$ adding the two equations, we get ##z=2##, We know that, $$iz+(3+i)w=-1+5i$$ $$⇒2i+(3+i)w=-1+5i$$...
  5. chwala

    Solve these simultaneous equations that involve vectors

    Find the question and solution here; Ok, i was able to solve this by using, ##3A=3ax+12ay+6bx+3by+3b## ##2B=2ay-4ax+4a+4bx-6by-2b## leading us to the simultaneous equation; ##7x+10y=4## ##2x+9b=-5## ##x=2## and ##y=-1## I had initially tried the approach of using ##3A=2B## →##B=1.5A## ...Then...
  6. D

    Solving these Simultaneous Equations

    Hi everyone Could someone please help with the above equation? Here is the working for my attempt ax + bx + cy = bc by + cy + ax = -ab ax + bx + cy = bc by + cy + ax = -ab b(x-y) = b(a + c) x - y = a + c a^2 + ac + ay + ab + bc + by + cy = bc a+2 + ac + ay + by + by = -ab...
  7. chwala

    Solve the simultaneous equations

    ##2^{x+y+1}##=##3^{x+y-1}## ##\frac {x+y+1}{x+y-1}##=##\frac {log 3}{log 2}## this is where i reached, i just got this problem from my old notes, i do not think we can solve this...
  8. hackedagainanda

    Simultaneous equations substitution method

    I'm really stuck on this one, I was able to get the answer but not by the substitution method. So its the weight as A and B so I get A + B = 24 A(3) = B(5) so in my head I calculate a few pairs, 3 x 5 = 15 but 3 + 5 only = 8 so the next pair would be 10 and 6 which is still to small so I move...
  9. AN630078

    How Do You Solve Simultaneous Equations for Time and Distance in a Car Journey?

    Equation 1: Where t1=time spent on motorway Where t2=time spent on country roads t1+t2=4 Equation 2: Using distance = speed * time 200 = 70*t1+40*t2 Rearrange equation 1 in terms of t1; t1=4-t2 Substitute the rearranged form of equation 1 into equation 2: 200=70(4-t2)+40t2 200=280-70t2+40t2...
  10. anemone

    MHB Prove Simultaneous Equations: $a+b+c+d \ne 0$

    The real numbers $a,\,b,\,c$ and $d$ satisfy the following simultaneous equations: $abc-d=1\\bcd-a=2\\cda-b=3\\dab-c=-6$ Prove that $a+b+c+d \ne 0$.
  11. hackedagainanda

    Simultaneous Equations Alternate Approach

    (55x + 45y) = 520 (1) (45x + 55y) = 480 (2) So first I notice they are divisible by 5 so I go ahead and do that. (11x + 9y) = 104 (1) (9x + 11y) = 96 (2) 11 times 9 is 99 and 9 times 11 is 99 so I can cancel some terms. I proceed to do that by multiplying the top by 11 and getting: (121x +...
  12. chwala

    Do simultaneous equations always have a unique solution?

    ...##2y-2z-2mz=6## ## 2y-2z-2mz= mx+8y+5z## i then let, ##-2z-2mz=5z## ##m=-7/2## ##→2y=mx+8y## ##7x=12y##
  13. R

    Derivation from simultaneous equations (Fabry-Perot etalon)

    Here are three equations: $$E_{2}=rE_{1}+itE_{3} \tag{1}$$ $$E_{4}=rE_{3}+itE_{1} \tag{2}$$ $$E_{2}=\tau\exp\left(i\varphi\right)E_{4} \tag{3}$$ I started by substituting Eqn. 3 into Eqn. 2, $$\frac{E_{2}}{\tau}\exp\left(-i\varphi\right)=rE_{3}+itE_{1}, \ \therefore E_{3} =...
  14. K

    Mesh Analysis AC, solving simultaneous equations....

    Homework Statement Hi guys I'm doing the mesh analysis of AC circuit and looking for some guidance. Here is the mesh picture and some components data: Homework Equations Kirchoff's voltage law and current law.The Attempt at a Solution I decided that mesh currents are going in clockwise...
  15. X

    Planetary gearbox speed calculation - Simultaneous equations

    I'm looking to calculate the ratio of a planetary gear train. With the ultimate goal of producing a spreadsheet/calculator to show the state of the gearbox (i.e. all shaft speeds) based on applied constraints. A gear set consists of Ring Gear, Planet Gear, Sun Gear. The sick diagram is the...
  16. yecko

    (Matlab) beam deflection solution using symbolic simultaneous equations

    I have tried to searched for functions online and apply it, but still it does not work well. May I ask how can I solve symbolic simultaneous equations with Matlab? Or is there anything went wrong with my program? Homework Statement Consider a stepped beam shown in below. The beam is...
  17. L

    MHB Standard formula for solving simultaneous equations of the form ax + by + c = 0

    Hello, This algorithm overall is probably more complicated than is correct for the pre-university forum but this question is about a relatively simple aspect of the calculations so I hope that this will be the proper place to ask. I am writing a little program to do some computational geometry...
  18. chwala

    Solving four variable simultaneous equations

    Homework Statement given ##mx + ny =7## ##mx^2 + ny^2=49## ##mx^3+ny^3=133## ##mx^4+ny^4=406## find ##2014(x+y-xy)-100(m+n)## Homework EquationsThe Attempt at a Solution ##(mx+ny)(mx-ny)=7(mx-ny)## ##m^2x^2-n^2y^2=7(mx-ny)## ##mx^2+ny^2=49##[/B]
  19. B

    I Notation for systems of simultaneous equations

    What notation would I need to use in order to write a mathematical statement to define a System S of simultaneous equations - let's say ax+by=c and ex+fy=g.
  20. B

    MHB What are the steps to solving simultaneous equations using substitution?

    hi could anyone help with this one as i do not know the steps to take . as far as i know you can only use substitution 4y^2-3x^2=1 x-2y=1
  21. whatphysics

    How do you work out simultaneous eqns w/ complex numbers & phasor

    I'm having trouble figuring out to get the answers from the 2 equations. The phasors and complex numbers confuse me. Do I need to change the phasor form? How do I go about doing this thanks! (Not homework question I am trying to figure this for my exam!)
  22. Rococo

    Algebra simultaneous equations Question

    Homework Statement Let ##g_k = 2cos(k/2)## and ##z=e^{ip(N+1)}## where N is an integer. There are two simultaneous equations: ##E^2 = (g_k + e^{ip})(g_k + e^{-ip}) = 1 + g_k^2 + 2g_k cos(p) ## [1] ##(1+z^2)E^2 = (g_k + e^{-ip})^2 z^2 + (g_k + e^{ip})^2##[2]...
  23. S

    I Solving simultaneous equations with matrix

    i don't understand how to get second box using first box in the picthure that has attached.could someone help me?
  24. M

    MHB Simultaneous equations number problem

    A certain numbers tenth place digit is $x$ & unit place digit is $1$. That number can be written as $(10x+y)$ . The sum of those two digits is 15 . When those two digits are flipped a number is made, That number less the first number results in 27. What Have I done so far $10x+y=15$...
  25. M

    MHB Construct a pair of simultaneous equations

    The students in a hostel are to get new uniforms. Each girl is to receive a blouse and a skirt , each boy is to receive a shirt and a pair of trousers.1 meter of white material is required to sew a blouse and $1\frac{1}{2}$ meters of blue material is required to sew a shirt . Moreover...
  26. L

    MHB Complex numbers simultaneous equations

    Hi all, I have spent a couple of hours on this perplexing question. Solve the simultaneous equations: z = w + 3i + 2 and z2 - iw + 5 - 2i = 0 giving z and w in the form (x + yi) where x and y are real. I tried various methods, all to no avail. I have substituted z into z2 , I got the wrong...
  27. M

    MHB Problem on Simultaneous equations

    There is a number between 100 and 1000. Its middle digit is 0.sum of the rest , first and last digits is 11.The number which gets by exchanging the first digit and the last digit is greater than by 495 from the previous number I. Build up an equation for the sum of first digit and the last...
  28. M

    Newtonian Mechanics: simultaneous equations

    Homework Statement Figure 5-12 shows a block S (the sliding block) with mass M 3.3 kg. The block is free to move along a horizontal frictionless surface and connected, by a cord that wraps over a frictionless pulley, to a second block H (the hanging block), with mass m 2.1 kg. The cord and...
  29. Biker

    B Algebra question -- Solving 2 simultaneous equations....

    It is a bit of a long question about series, But what is important is this... a+ 2c = 3b (3b-2)^2 = 2a * (4c-2) It is asking for the ratio c to a It have tried a lot of ways. I always end up with this. (Note maybe I not noticing a mistake, Can just anyone confirm that this is solvable? )...
  30. B

    Is there an easier way to do this question about series?

    Hey guys, the question is 6.b. in the picture : http://imgur.com/FaKUMUZ Here is what I did to solve it : http://imgur.com/YrIvbTO I made these two simultaneous equations. 1875 comes from the fact that U1 + U2 = 1500 and U3 + U4 = 375. Then S4 must equal 1500+ 375(1875). I then found a formula...
  31. G

    MHB Solve Simultaneous Equations: No/1/Inf Solns?

    $x+2y-z=2 \\ x-y+z =5 \\ 3x+3y-z=\mu$ The question is for what value of the parameter has the equation (a) no solutions, (b) one solution, and (c) infinitely many solutions. The trouble when I solve this system using guassian elimination I get $ (x, y, z) = ( -19-\frac{1}{2}\mu, 7...
  32. D

    General Solution To Three Simultaneous Equations

    I herewith submit for reference, review and comment the general solution to 3 simultaneous equations as follows:
  33. M

    Simultaneous Equations (How to test for redundancy)

    Homework Statement I have three equations: ## F = ρw(x_0 y^2_0 - x_1 y^2_1) + \frac{1}{2} γ w (x^2_0 - x^2_1)## ----- 1 ##y_0 = y_1 \frac{x_1}{x_0}## ----- 2 ##\frac{y^2_0}{2} + gx_0 = \frac{y^2_1}{2} + gx_1## ------ 3 Homework Equations N/A The Attempt at a Solution My goal is to have...
  34. kostoglotov

    How are the x1 and x4 values determined in the solution to the matrix equation?

    Hi, rapid fire posting in this subforum I know, sorry if that's annoying. Let me know if I should space my posts out a bit more. Here's an image of the solution to a worked example (from Intro to Linear Algebra 4th by Strang) here's the imgur link: http://i.imgur.com/IG6r15H.jpg I cannot...
  35. P

    Can you solve this system of simultaneous equations?

    hello! I am really wondering what is going on here let's say we have 3 equations: with x, y, z to be our unknowns and the rest regular integers a*x+b*y-c*z=0 d*x-e*y+f*z=0 g*x+h*y+i*z=0 the signs of each integer may be positive or negative is there a solution to this system of equations or...
  36. S

    Can Factoring Simplify Complex Algebraic Equations?

    Homework Statement I was asked to solve this equation: ##{(x-\frac{1}{y})}^{2} -(y-\frac{1}{x})(x-\frac{1}{y})=9x## ##x-y=1## Homework Equations Simultaneous equations, factor theorem and quadratic formula The Attempt at a Solution I know I could have solved for x in the second equation, and...
  37. chwala

    Solving simultaneous equations

    I am trying to solve the simultaneous equation 2^x+y = 6^y and 3^x = 6(2^y) i have solved as follows 3^x . 2^x+y = 3^x . 6^y 3^x. 2^x+y = 6(2^y). 2^x+y on subtraction i get 3^x.6^y - 6(2^y).2^x+y = 0 then 3^x. 6^y = 6(2^y). 2^x. 2^y on solving i get x log (3/2)= log 6+y log(3/2) now i do i...
  38. anemone

    MHB Simultaneous Equations Challenge II

    Solve for real solutions of the system of equations below: $a(\sqrt{b}+b)=\sqrt{1-a}(\sqrt{a}+\sqrt{1-a})$ $32a(a^2-1)(2a^2-1)^2+b=0$
  39. anemone

    MHB Simultaneous Equations Challenge

    Solve the system of equations below: $(a+\sqrt{a^2+1})(b+\sqrt{b^2+1})=1$ $b+\dfrac{b}{\sqrt{a^2-1}}+\dfrac{35}{12}=0$
  40. A

    Simultaneous Equations and Fields

    Homework Statement What does it mean that basic arithmetic can be performed with two (non parallel) linear equations and that the resulting equation also intersects the same point? Proof and or anecdotal explanation would be much appreciated. Homework Equations If (α) 3y = 4x...
  41. A

    MHB How to Solve Simultaneous Equations with Multiplication Symbols?

    Can someone solve this, i know its not very hard but for me it is :/ The dot . is meaned to be * (multiplication) can someone help me :)
  42. A

    Solving simultaneous equations

    Homework Statement A uniaxial crystal of indices n0 and ne is cut so that the optic axis is perpendicular to the surface. Show that for light from the outside at an angle of incidence θi, the angle of refraction of the e-ray is Homework Equations The Attempt at a Solution I solved for...
  43. L

    MHB Solve Simultaneous Equations y=2x²+3x-31 & y=21-2x

    y=2x²+3x-31 y=21-2x solve for x and y
  44. anemone

    MHB Solving Simultaneous Equations: x⁴-y²-xy=4-√15, x³+y³-3x=5√5

    Hi MHB, I hope to gain some insights on how to solve this system of equations because I tried it many times to use trigonometric approach but to no avail...:mad: Problem: Solve the system of equations $x^4-y^2-xy=4-\sqrt{15}$ $x^3+y^3-3x=5\sqrt{5}$ Attempt: At first glance, $x^3-3x$...
  45. anemone

    MHB Unsolvable Simultaneous Equations: A Mathematician's Dilemma

    Hi MHB, For the first time I found a system of equations where I'm at my wit's end and don't know how to solve it, no matter how hard I tried... Problem: Solve z^2+2xyz=1 3x^2y^2+3xy^2=1+x^3y^4 z+zy^4+4y^3=4y+6y^2z Attempt: I tried to eliminate the variable $z$ and obtained another...
  46. anemone

    MHB Simultaneous Equations Challenge

    Solve the following system in real numbers: a^2+b^2=2c 1+a^2=2ac c^2=ab
  47. M

    MHB Solve Worded Simultaneous Equations: Tips & Examples

    Hello, I am going over past exam questions in preparation for exams and I am horrible at worded questions, can someone please give me some guidance in working out this equation? Or in general how to figure out how to solve worded simultaneous questions? Many thanks :) You have spent \$112 on...
  48. Albert1

    MHB Solving for simultaneous equations

    ( i ) prove the following simultaneous equations (1) (2) and (3) has no real solution $a+b+c=1-----(1)$ $a^2+b^2+c^2=2----(2)$ $a^3+b^3+c^3=3----(3)$ ( ii ) using (1)(2)and(3)find the value of : $a^4+b^4+c^4$
  49. B

    A three-gear alignment problem, simultaneous equations

    This is a problem that a few friends and I came up with while working on an extra-curricular robotics project: There are three gears meshed together with idle gears inbetween so that the three gears rotate in the same direction. http://puu.sh/2knXq The gear ratio between gear A has 4 teeth...