$\begingroup$ can you show an example of a direct equation you've resolved that has multiple solutions? $\endgroup$
If us assume that all linear equations have the form:
$$ax + b= 0$$
(which is fully valid and also should be exactly how we view direct equations)
then straight equations have actually either 1, 0, or limitless solutions. It"s quite straightforward if $a \neq 0$ climate they have exactly one solution: $x = -\fracba$.
You are watching: How many solutions does a linear equation have
On the other hand, if $a = 0$ then if $b = 0$ we have actually infinite options (any value of $x$ solves $0x + 0 = 0$) and also if $a = 0$ and $b \neq 0$ then there room no solutions (there is no value of $x$ that provides $0x + 1 = 0$, for example).
answered might 17 "16 at 2:55
5,86311 gold badge1616 silver badges1818 bronze badges
add a comment |
If we have actually $2$ unknowns, then the linear system
$$a_1 x_1 + a_2 x_2 = b$$
has, in general, infinitely countless solutions. Why is that? Assuming that $a_1 \neq 0$, we write
$$x_1 = \fracba_1 - \left(\fraca_2a_1\right) x_2$$
Let $x_2 = \gamma$, whereby $\gamma \in \sdrta.netbbR$. Then, the solution set is a line parameterized as follows
$$\beginbmatrixx_1\\ x_2\endbmatrix = \beginbmatrix \fracba_1\\ 0\endbmatrix + \gamma \beginbmatrix - \fraca_2a_1\\ 1\endbmatrix$$
answered may 17 "16 in ~ 3:11
Rodrigo de AzevedoRodrigo de Azevedo
| present 4 more comments
Thanks because that contributing an answer to sdrta.netematics stack Exchange!Please be sure to answer the question. Carry out details and share her research!
But avoid …Asking for help, clarification, or responding to other answers.Making statements based on opinion; earlier them up with references or an individual experience.
Use sdrta.netJax to layout equations. Sdrta.netJax reference.
To find out more, view our advice on writing good answers.
See more: How Many Cups In A Can Of Tuna ? How Many Cups Are In 1 Can Of Tuna
Sign increase or log in in
sign up utilizing Google
sign up utilizing Facebook
authorize up making use of Email and Password
Post as a guest
email Required, but never shown
Post as a guest
Required, however never shown
short article Your answer Discard
Not the prize you're spring for? Browse various other questions tagged algebra-precalculus or ask your own question.
Featured top top Meta
straight equation is equal to a cubic equations, inquiry about variety of solutions?
an oddity in some linear equations
How countless solutions for this equation?
how do I fix two equations in 2 unknowns?
Graphing systems of straight equations.
addressing a solution of equations to disprove one inequality
species of services to $n$ straight Equations v $n$ Unknowns
How have the right to I uncover all possible solutions that a trigonometric equation?
warm Network questions more hot concerns
subscribe to RSS
inquiry feed To i ordered it to this RSS feed, copy and paste this URL right into your RSS reader.
stack Exchange Network
site design / logo design © 2021 ridge Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.10.13.40448