Simultaneous equations Definition and 124 Threads

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...

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 $a+b+c+d \ne 0$.

(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 +...

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

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...

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...

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]

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.

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

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]...

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

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...

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

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...

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

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

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...

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 :)

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...

y=2x²+3x-31 y=21-2x solve for x and y

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...

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

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...

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...