Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{c+3b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&b=-\frac{c}{3}\text{ and }x=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{c+3b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&b=-\frac{c}{3}\text{ and }x=0\end{matrix}\right.
Solve for b
b=\frac{-ax-c}{3}
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ax+c=-3b
Subtract 3b from both sides. Anything subtracted from zero gives its negation.
ax=-3b-c
Subtract c from both sides.
xa=-3b-c
The equation is in standard form.
\frac{xa}{x}=\frac{-3b-c}{x}
Divide both sides by x.
a=\frac{-3b-c}{x}
Dividing by x undoes the multiplication by x.
a=-\frac{c+3b}{x}
Divide -3b-c by x.
ax+c=-3b
Subtract 3b from both sides. Anything subtracted from zero gives its negation.
ax=-3b-c
Subtract c from both sides.
xa=-3b-c
The equation is in standard form.
\frac{xa}{x}=\frac{-3b-c}{x}
Divide both sides by x.
a=\frac{-3b-c}{x}
Dividing by x undoes the multiplication by x.
a=-\frac{c+3b}{x}
Divide -3b-c by x.
3b+c=-ax
Subtract ax from both sides. Anything subtracted from zero gives its negation.
3b=-ax-c
Subtract c from both sides.
\frac{3b}{3}=\frac{-ax-c}{3}
Divide both sides by 3.
b=\frac{-ax-c}{3}
Dividing by 3 undoes the multiplication by 3.
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y = 3x + 4
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Matrix
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Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}