Solve for m (complex solution)
\left\{\begin{matrix}m=-\frac{3x-y+2}{2x}\text{, }&x\neq 0\\m\in \mathrm{C}\text{, }&y=2\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{2-y}{2m+3}\text{, }&m\neq -\frac{3}{2}\\x\in \mathrm{C}\text{, }&y=2\text{ and }m=-\frac{3}{2}\end{matrix}\right.
Solve for m
\left\{\begin{matrix}m=-\frac{3x-y+2}{2x}\text{, }&x\neq 0\\m\in \mathrm{R}\text{, }&y=2\text{ and }x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{2-y}{2m+3}\text{, }&m\neq -\frac{3}{2}\\x\in \mathrm{R}\text{, }&y=2\text{ and }m=-\frac{3}{2}\end{matrix}\right.
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y=2mx+3x+2
Use the distributive property to multiply 2m+3 by x.
2mx+3x+2=y
Swap sides so that all variable terms are on the left hand side.
2mx+2=y-3x
Subtract 3x from both sides.
2mx=y-3x-2
Subtract 2 from both sides.
2xm=-3x+y-2
The equation is in standard form.
\frac{2xm}{2x}=\frac{-3x+y-2}{2x}
Divide both sides by 2x.
m=\frac{-3x+y-2}{2x}
Dividing by 2x undoes the multiplication by 2x.
y=2mx+3x+2
Use the distributive property to multiply 2m+3 by x.
2mx+3x+2=y
Swap sides so that all variable terms are on the left hand side.
2mx+3x=y-2
Subtract 2 from both sides.
\left(2m+3\right)x=y-2
Combine all terms containing x.
\frac{\left(2m+3\right)x}{2m+3}=\frac{y-2}{2m+3}
Divide both sides by 2m+3.
x=\frac{y-2}{2m+3}
Dividing by 2m+3 undoes the multiplication by 2m+3.
y=2mx+3x+2
Use the distributive property to multiply 2m+3 by x.
2mx+3x+2=y
Swap sides so that all variable terms are on the left hand side.
2mx+2=y-3x
Subtract 3x from both sides.
2mx=y-3x-2
Subtract 2 from both sides.
2xm=-3x+y-2
The equation is in standard form.
\frac{2xm}{2x}=\frac{-3x+y-2}{2x}
Divide both sides by 2x.
m=\frac{-3x+y-2}{2x}
Dividing by 2x undoes the multiplication by 2x.
y=2mx+3x+2
Use the distributive property to multiply 2m+3 by x.
2mx+3x+2=y
Swap sides so that all variable terms are on the left hand side.
2mx+3x=y-2
Subtract 2 from both sides.
\left(2m+3\right)x=y-2
Combine all terms containing x.
\frac{\left(2m+3\right)x}{2m+3}=\frac{y-2}{2m+3}
Divide both sides by 2m+3.
x=\frac{y-2}{2m+3}
Dividing by 2m+3 undoes the multiplication by 2m+3.
Examples
Quadratic equation
{ 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}