Solve for k (complex solution)
\left\{\begin{matrix}k=-\frac{5-y-3x}{2x}\text{, }&x\neq 0\\k\in \mathrm{C}\text{, }&y=5\text{ and }x=0\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{5-y}{2k-3}\text{, }&k\neq \frac{3}{2}\\x\in \mathrm{C}\text{, }&y=5\text{ and }k=\frac{3}{2}\end{matrix}\right.
Solve for k
\left\{\begin{matrix}k=-\frac{5-y-3x}{2x}\text{, }&x\neq 0\\k\in \mathrm{R}\text{, }&y=5\text{ and }x=0\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{5-y}{2k-3}\text{, }&k\neq \frac{3}{2}\\x\in \mathrm{R}\text{, }&y=5\text{ and }k=\frac{3}{2}\end{matrix}\right.
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y=2kx-3x+5
Use the distributive property to multiply 2k-3 by x.
2kx-3x+5=y
Swap sides so that all variable terms are on the left hand side.
2kx+5=y+3x
Add 3x to both sides.
2kx=y+3x-5
Subtract 5 from both sides.
2xk=3x+y-5
The equation is in standard form.
\frac{2xk}{2x}=\frac{3x+y-5}{2x}
Divide both sides by 2x.
k=\frac{3x+y-5}{2x}
Dividing by 2x undoes the multiplication by 2x.
y=2kx-3x+5
Use the distributive property to multiply 2k-3 by x.
2kx-3x+5=y
Swap sides so that all variable terms are on the left hand side.
2kx-3x=y-5
Subtract 5 from both sides.
\left(2k-3\right)x=y-5
Combine all terms containing x.
\frac{\left(2k-3\right)x}{2k-3}=\frac{y-5}{2k-3}
Divide both sides by 2k-3.
x=\frac{y-5}{2k-3}
Dividing by 2k-3 undoes the multiplication by 2k-3.
y=2kx-3x+5
Use the distributive property to multiply 2k-3 by x.
2kx-3x+5=y
Swap sides so that all variable terms are on the left hand side.
2kx+5=y+3x
Add 3x to both sides.
2kx=y+3x-5
Subtract 5 from both sides.
2xk=3x+y-5
The equation is in standard form.
\frac{2xk}{2x}=\frac{3x+y-5}{2x}
Divide both sides by 2x.
k=\frac{3x+y-5}{2x}
Dividing by 2x undoes the multiplication by 2x.
y=2kx-3x+5
Use the distributive property to multiply 2k-3 by x.
2kx-3x+5=y
Swap sides so that all variable terms are on the left hand side.
2kx-3x=y-5
Subtract 5 from both sides.
\left(2k-3\right)x=y-5
Combine all terms containing x.
\frac{\left(2k-3\right)x}{2k-3}=\frac{y-5}{2k-3}
Divide both sides by 2k-3.
x=\frac{y-5}{2k-3}
Dividing by 2k-3 undoes the multiplication by 2k-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}