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
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...
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##...
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...
$$(1+i)z+(2-i)w=3+4i$$
$$iz+(3+i)w=-1+5i$$
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, $$iz+(3+i)w=-1+5i$$
$$⇒2i+(3+i)w=-1+5i$$...
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...
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...
##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...
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...
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...
(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 +...
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} =...
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...
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...
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...
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...
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.
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!)
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]...
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
$10x+y=15$...
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...
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...
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...
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...
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? )...
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...
$x+2y-z=2 \\
x-y+z =5 \\
3x+3y-z=\mu$
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...
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...
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...
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...
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...
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...
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...
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...
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, $x^3-3x$...
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...
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...
( 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 :
$a^4+b^4+c^4$
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...