Systems of Equations Questions and Answers

Recent questions in Systems of equations

$EXP=\left\{\begin{array}{ll}{n}^{3}\left(\frac{⌊\frac{n+1}{3}⌋+24}{50}\right)& n\le 15\\ {n}^{3}\left(\frac{n+14}{50}\right)& 15\le n\le 36\\ {n}^{3}\left(\frac{⌊\frac{n}{2}⌋+32}{50}\right)& 36\le n\le 100\end{array}$In this equation there are 3 systems of equations, but there are inequalities next to them. Does this mean that for example we use the top equation when$n\le 15\phantom{\rule{0ex}{0ex}}$and so on?

Alani Conner 2022-05-23 Answered

For which value(s) of parameter m is there a solution for this system$\left\{\begin{array}{l}mx+y=m\\ mx+2y=1\\ 2x+my=m+1\end{array}$when does this system of equations have a solution?

Case Nixon 2022-05-23 Answered

Simultaneous equation difficulty minus$\left(1\right)×3$$\left(3\right)-\left(2\right)$$21x=-7$$3x=-1$

Brooke Webb 2022-05-23 Answered

Is the following equation regarded as a linear equation?$0{x}_{1}+0{x}_{2}+0{x}_{3}=5$The original question is as below:Solve the linear system given by the following augmented matrix:$\left(\begin{array}{cccc}2& 2& 3& 1\\ 2& 5& 3& 0\\ 0& 0& 0& 5\end{array}\right)$Note the words linear system in the original question. So, I was asking myself whether $0{x}_{1}+0{x}_{2}+0{x}_{3}=5$ is a linear equation. Can we call all of the equations given by the matrix collectively as a linear system?

Brennen Fisher 2022-05-22 Answered

choosing $h$and $k$ such that this system:$\left\{\begin{array}{l}{x}_{1}+h{x}_{2}=2\\ 4{x}_{1}+8{x}_{2}=k\end{array}$Has (a) no solution, (b) a unique solution, and (c) many solutions.First i made an augmented matrix, then performed row reduction:$\left[\begin{array}{ccc}1& h& 2\\ 4& 8& k\end{array}\right]\sim \left[\begin{array}{ccc}1& h& 2\\ 0& 8-4h& k-8\end{array}\right]$Continuing row reduction, i get:$\sim \left[\begin{array}{ccc}1& 0& \frac{k-8}{2\left(h-2\right)}+\frac{k}{4}\\ 0& 1& \frac{k-8}{8-4h}\end{array}\right]$how to go about solving the problem with the matrix i end up with?

Rachel Villa 2022-05-22 Answered

how to resolve this system of differential equations of order 1?$\left\{\begin{array}{ccc}{\stackrel{˙}{p}}_{1}& =& \frac{1}{z}{p}_{2}{p}_{3}\\ {\stackrel{˙}{p}}_{2}& =& -\frac{1}{z}{p}_{1}{p}_{3}\\ {\stackrel{˙}{p}}_{3}& =& \left(\frac{1}{y}-\frac{1}{x}\right){p}_{1}{p}_{2}\end{array}$where ${p}_{1}\left(0\right)=a,{p}_{2}\left(0\right)=b,{p}_{3}\left(0\right)=c$ and $x,y,z$ are constants.1) how to resolve this system differential equations by hand?2) what if $x=y=M$ where $M$ is a constant?

Andy Erickson 2022-05-22 Answered

Solving a set of recurrence relations${A}_{n}={B}_{n-1}+{C}_{n-1}$${B}_{n}={A}_{n}+{C}_{n-1}$${C}_{n}={B}_{n}+{C}_{n-1}$${D}_{n}={E}_{n-1}+{G}_{n-1}$${E}_{n}={D}_{n}+{F}_{n-1}$${F}_{n}={G}_{n}+{C}_{n}$${G}_{n}={E}_{n}+{F}_{n-1}$which I would like to solve, with the goal of eventually finding an explicit form of ${E}_{n}$. I started out by looking at only ${A}_{n}$, ${B}_{n}$ and ${C}_{n}$, and found a formula for ${A}_{n}$.${A}_{n}=1/3\sqrt{3}\left(2+\sqrt{3}{\right)}^{n}-1/3\sqrt{3}\left(2-\sqrt{3}{\right)}^{n}$but I cant seem to find the right trick this time.

Nylah Burnett 2022-05-21 Answered

System of ODEs with productsHow can we solve the system of differential equations$\frac{df\left(t\right)}{dt}=-f\left(t\right)h\left(t\right),\frac{dg\left(t\right)}{dt}=-g\left(t\right)h\left(t\right),\frac{dh\left(t\right)}{dt}=1-\left(h\left(t\right){\right)}^{2}$The system does not fall to standard ODE methods.

Isaiah Owens 2022-05-21 Answered

$M=1+\frac{a}{b}$$S=a+b$So, I put it up like this:$1+\frac{a}{b}=a+b$If $M=S$, how to isolate $a$?

Kiana Harper 2022-05-21 Answered

Find m to the equation:$\left\{\begin{array}{l}2{x}^{3}-\left(y+2\right){x}^{2}+xy=m\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\left(1\right)\\ {x}^{2}+x-y=1-2m\phantom{\rule{thinmathspace}{0ex}}\phantom{\rule{thinmathspace}{0ex}}\left(2\right)\end{array}$My try: From $\left(1\right)$ and $\left(2\right)\phantom{\rule{thinmathspace}{0ex}}⇒$:$4{x}^{3}-2\left(y+2\right){x}^{2}+2xy+{x}^{2}+x-y=1\phantom{\rule{0ex}{0ex}}⇔4{x}^{3}-3{x}^{2}+x-1=y\left(2{x}^{2}-2x+1\right)\phantom{\rule{0ex}{0ex}}⇔y=\frac{4{x}^{3}-3{x}^{2}+x-1}{2{x}^{2}-2x+1}\phantom{\rule{0ex}{0ex}}⇔y=2x+\frac{1}{2}-\frac{3}{2\left(2{x}^{2}-2x+1\right)}$From $\left(2\right)\phantom{\rule{thinmathspace}{0ex}}⇒$$2m=1+y-{x}^{2}-x\phantom{\rule{0ex}{0ex}}=1+2x+\frac{1}{2}-\frac{3}{2\left(2{x}^{2}-2x+1\right)}-{x}^{2}-x\phantom{\rule{0ex}{0ex}}=-{x}^{2}+x+\frac{3}{2}-\frac{3}{2\left(2{x}^{2}-2x+1\right)}$And I don't know how to contine,The result is: $m\le 1-\frac{\sqrt{3}}{2}$

Shamar Reese 2022-05-21 Answered

Solve following series of equations ($n+2$ equations $n+2$ variables):${k}_{0}{q}_{0}+\lambda {q}_{0}+{c}_{0}=0,\phantom{\rule{0ex}{0ex}}{k}_{1}{q}_{1}+\lambda {q}_{1}+{c}_{1}=0,\phantom{\rule{0ex}{0ex}}{k}_{n}{q}_{n}+\lambda {q}_{n}+{c}_{n}=0,\phantom{\rule{0ex}{0ex}}{q}_{1}+{q}_{2}+....+{q}_{n}=1.$The variables are ${q}_{0},{q}_{1},.....,{q}_{n}$ and $\lambda$. Note that $k$ and $c$ are series of constants.

Trevor Wood 2022-05-21 Answered

Applications of polynomial systems of equationsWhat are some applications of Polynomial Systems of Equations?

Marianna Stone 2022-05-21 Answered

How to solve coupled linear 1st order PDEIt is fairly straight forward to solve linear 1st order PDEs by the method of characteristics. For example, if${\mathrm{\partial }}_{t}f+a{\mathrm{\partial }}_{x}f=bf$we have that $\frac{df}{dt}=bf$ on the characteristic curve of $\frac{dx}{dt}=a$. From this we deduce that $f\left(t,x\right)=g\left(C\right){e}^{bt}$ where $x=at+C$.Now, how does this work when $f$ is multidimensional. Can I solve equations on the following form by characteristics, or by any other means?${\mathrm{\partial }}_{t}{f}_{i}\left(t,x\right)+\sum _{j}{A}_{ij}{\mathrm{\partial }}_{x}{f}_{j}\left(t,x\right)=\sum _{j}{B}_{ij}{f}_{j}\left(t,x\right)$where the components of $A$ and $B$ might be dependent on $x$ and $t$.In particular, I am trying to solve the following,$\left\{\begin{array}{l}{\mathrm{\partial }}_{t}f+\frac{c}{t}{\mathrm{\partial }}_{x}g=-\left(a+\frac{1}{t}\right)f\\ {\mathrm{\partial }}_{t}g+\frac{c}{t}{\mathrm{\partial }}_{x}f=-\left(b+\frac{1}{t}\right)g\end{array}$where $f$ and $g$ are functions of $x$ and $t$ , where $t>{t}_{0}>0$, $c\ne 0$. Any help is highly appreciated.

Davin Fields 2022-05-21 Answered