# 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. ### 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. ### 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. ### 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. ### 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. ### 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. ### 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...

8. ### 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...
9. ### 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...
10. ### 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...
11. ### 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 $a+b+c+d \ne 0$.
12. ### 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 +...
13. ### 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##
14. ### 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} =...
15. ### 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...
16. ### 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...
17. ### (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...
18. ### 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...
19. ### 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]
20. 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.
21. ### 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
22. ### 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!)
23. ### 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]...
24. ### 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?
25. ### 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 $10x+y=15$...
26. ### 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...
27. ### 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...
28. ### 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...
29. ### 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...
30. ### 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? )...
31. ### 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...

49. ### 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 : $a^4+b^4+c^4$
50. ### 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...