My sdrta.net book says, a straight equation has precisely one solution. Because $ax + b = 0$; $x =-\fracba$. But I"ve solved countless linear equations with multiple services before. (I"m no very an excellent in sdrta.net. Require help...)  $\begingroup$ 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).

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answered might 17 "16 at 2:55 JaredJared
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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

$$\beginbmatrixx_1\\ x_2\endbmatrix = \beginbmatrix \fracba_1\\ 0\endbmatrix + \gamma \beginbmatrix - \fraca_2a_1\\ 1\endbmatrix$$

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answered may 17 "16 in ~ 3:11 Rodrigo de AzevedoRodrigo de Azevedo
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