Solve for a
\left\{\begin{matrix}\\a=-1\text{, }&\text{unconditionally}\\a\in \mathrm{R}\text{, }&b=1\end{matrix}\right.
Solve for b
\left\{\begin{matrix}\\b=1\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&a=-1\end{matrix}\right.
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-ab+a=b-1
Reorder the terms.
\left(-b+1\right)a=b-1
Combine all terms containing a.
\left(1-b\right)a=b-1
The equation is in standard form.
\frac{\left(1-b\right)a}{1-b}=\frac{b-1}{1-b}
Divide both sides by 1-b.
a=\frac{b-1}{1-b}
Dividing by 1-b undoes the multiplication by 1-b.
a=-1
Divide b-1 by 1-b.
\left(-a\right)b+a-b=-1
Subtract b from both sides.
\left(-a\right)b-b=-1-a
Subtract a from both sides.
-ab-b=-a-1
Reorder the terms.
\left(-a-1\right)b=-a-1
Combine all terms containing b.
\frac{\left(-a-1\right)b}{-a-1}=\frac{-a-1}{-a-1}
Divide both sides by -a-1.
b=\frac{-a-1}{-a-1}
Dividing by -a-1 undoes the multiplication by -a-1.
b=1
Divide -a-1 by -a-1.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
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}