I have the following equations:  $$8\equiv-(3a+7b)\mod11$$ and $$9\equiv-(5a+4b)\mod11$$  How do I solve them? I've tried to subtract one equation from the other, but I end up with the wrong answer.  It is supposed to be: $a=2$ and $b=9$.
The problem I am given is finding a solution to the following pair of equations:  $3x + 4y$ $\equiv$ $5$ $mod$ $13$  $2x + 5y$ $\equiv$ $7$ $mod$ $13$  By reading the methodology here:   Since the modulos in my problem are also the same, I am able to use substitution, but this leaves fractions in my expressions.  I then used matrix multiplication as follows:  $\begin{bmatrix} 3 &amp; 4\\ 2 &amp; 5\end{bmatrix}$ $\begin{bmatrix}\ x\\ y\end{bmatrix}$ = $\begin{bmatrix}\ 5\\ 7\end{bmatrix}$   And solving this also gives me a matrix with fractions, so I am a bit lost on how to solve this problem.  Any help is appreciated. Thank you very much.
Extracting Data Between two Characters in Excel I have the following format in Excel and I am trying to extract the data between the characters:  First Last &lt;flastname@xxxx.com&gt;   I need to extract the email address between &lt; and > into its own cell  Thanks! What is dependency injection? There have been several questions already posted with specific questions about , such as when to use it and what frameworks are there for it. However,  What is dependency injection and when/why should or shouldn't it be used? Prove that:$\int_{a}^{b} f(x) dx = b \cdot f(b) - a \cdot f(a) - \int_{f(a)}^{f(b)} f^{-1}(x) dx$ How to get my software into Ubuntu? Problem with PDO MySQL Bevel is not symmetrical Does the sum of reciprocals of primes converge? Is this series known to converge, and if so, what does it converge to (if known)?  Where $p_n$ is prime number $n$, and $p_1 = 2$,  $$\sum\limits_{n=1}^\infty \frac{1}{p_n}$$ How am I to "[u]se induction to show that $n$ straight lines in the plane divide the plane into $\frac{n^2+n+2}{2}$ regions"? It is assumed here that no two lines are parallel and that no three lines have a common point. Further, this is not a non-Euclidean problem, but I wouldn't mind a discussion on the non-Euclidean nature of the problem.  I was thinking it might be easier to show using the unit sphere.    A GOOD REFERENCE I FOUND THAT WILL BE USEFUL TO ANYONE COMING ACROSS THIS PROBLEM IS Concrete Mathematics, Graham, Knuth, Patashnik pp. 4–8. This was working perfectly on 17.10 but after upgrading to 18.04 yesterday, when the lid is closed the screen turns off but doesn't suspend properly.  I travel around a lot and immediately noticed the heat (and battery draining) when taking it out of the travel case.  I've tried uncommenting these lines in /etc/systemd/logind.conf  HandleLidSwitch=suspend HandleLidSwitchDocked=suspend   and restarted but didn't make any difference. How to execute code after html form reset with jquery? Is it possible to automatically "add" \left and \right commands in front of all brackets? The source code should be left intact, but LaTeX should interpret every pair of brackets as if they were preceded by such commands. This is because adding \left and \right commands is time consuming and makes source code longer and less readable. I considered defining new commands such as \lb and \rb for \left( and \right), but it doesn't seem very elegant to me: what if I also want to add square brackets for example?  Any ideas? Thanks. Why is $5^{n+1}+2\cdot 3^n+1$ a multiple of $8$ for every natural number $n$? 'undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' while compiling bochs I'm trying to compile bochs with this command:  ./configure --with-x11 --with-wx --enable-ne2000 --enable-iodebug --enable-disasm --enable-debugger --enable-e1000 --enable-usb --enable-pci   it works, but then when I run make I got:  usr/bin/ld: gui/libgui.a(gtk_enh_dbg_osdep.o): undefined reference to symbol 'pthread_create@@GLIBC_2.2.5' /lib/x86_64-linux-gnu/libpthread.so.0: error adding symbols: DSO missing from command line   Any Help ? :/ Most descriptions of SIGTERM and SIGKILL point out that SIGKILL,     In contrast to SIGTERM and SIGINT, [...] cannot be caught or ignored [...] ()   Is this the only difference between SIGTERM and SIGKILL? In particular, if a process does not install a SIGTERM handler, is there any difference at all between sending SIGTERM or SIGKILL to the process? Without appealing to the axiom of choice, it can be shown that (Proposition:) if $X$ is well-orderable, then $2^X$ is totally-orderable.  Question: can we show the stronger result that if $X$ is well-orderable, then so too is $2^X$?  Proof of Proposition. Pick any well-ordering of $X$. Then the lexicographic order totally orders $2^X$.  More explicitly: for any two $f,g \in 2^X$, define $f &lt; g$ iff   there exists $x \in X$ such that $f(x) \neq g(x)$, and if $x \in X$ is minimal such that $f(x) \neq g(x)$, then $f(x)=0$ and $g(x)=1$.   It can be shown that $&lt;$ totally-orders $2^X$. Does $1.0000000000\cdots 1$ with an infinite number of $0$ in it exist? The situation is my  has been enchanted with .  The creature has      when it dies, return it to his owner’s hand   The enchantment says     When enchanted creature dies, return that card to the battlefield under your control with a +1/+1 counter on it.   Who gets the creature? Me or my rival?  Does the creature ability trigger before or after enchantment? This is my first post on this forum :)  I've been trying for a while to solve this problem about symmetric difference of two sets:     Given two sets $A$ and $B$, we call symmetric difference of $A$ and $B$ the following:      $$A\mathrel{\triangle}B = (A\cup B)-(A\cap B)$$      Show that if $A\mathrel{\triangle} B = \emptyset$, then $(A\subset B) \vee (B\subset A)$.   I don’t know where to start; thank you very much for the help :) What's wrong with this experiment showing that either FTL communication is possible or complementarity doesn't hold? The assumptions are:    Alice and Bob have perfectly synchronized clocks Alice and Bob have successfully exchanged a pair of entangled photons   The idea is simply to have Alice and Bob perform the Quantum Eraser Experiment (doesn't need to be the delayed choice).   Alice and Bob agree on a specific time when Bob's photon will be between the "path marker" (which is usually just after the slits) and the detector.  If Alice acts collpasing the wave-function on her photon, the interference pattern will disappear. If not it won't.  Alice and Bob can be spatially separated...  What am I misunderstanding?   The only meaningful difference from this spatially separated quantum eraser experiment to one done on tabletop is that you won't be able to use a coincidence detector, but that is not impeditive to identifying the interference pattern, just will make errors more probable. Which we should be able to deal with a appropriate protocol...  There is a experimental paper with a small amount of citations pointing out to the breaking of complementarity in a very similar setup: Where do I get a SIS mirage 672 vga driver?