Solve for a
\left\{\begin{matrix}a=-b+\frac{y}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
Solve for b
\left\{\begin{matrix}b=-a+\frac{y}{x}\text{, }&x\neq 0\\b\in \mathrm{R}\text{, }&y=0\text{ and }x=0\end{matrix}\right.
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y=xa+xb
Use the distributive property to multiply x by a+b.
xa+xb=y
Swap sides so that all variable terms are on the left hand side.
xa=y-xb
Subtract xb from both sides.
xa=y-bx
The equation is in standard form.
\frac{xa}{x}=\frac{y-bx}{x}
Divide both sides by x.
a=\frac{y-bx}{x}
Dividing by x undoes the multiplication by x.
a=-b+\frac{y}{x}
Divide y-bx by x.
y=xa+xb
Use the distributive property to multiply x by a+b.
xa+xb=y
Swap sides so that all variable terms are on the left hand side.
xb=y-xa
Subtract xa from both sides.
xb=y-ax
The equation is in standard form.
\frac{xb}{x}=\frac{y-ax}{x}
Divide both sides by x.
b=\frac{y-ax}{x}
Dividing by x undoes the multiplication by x.
b=-a+\frac{y}{x}
Divide y-ax by x.
Examples
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{ x } ^ { 2 } - 4 x - 5 = 0
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Linear equation
y = 3x + 4
Arithmetic
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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}