Solve for a (complex solution)
\left\{\begin{matrix}a=\frac{3y+5}{2x+1}\text{, }&x\neq -\frac{1}{2}\\a\in \mathrm{C}\text{, }&y=-\frac{5}{3}\text{ and }x=-\frac{1}{2}\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{-3y+a-5}{2a}\text{, }&a\neq 0\\x\in \mathrm{C}\text{, }&y=-\frac{5}{3}\text{ and }a=0\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=\frac{3y+5}{2x+1}\text{, }&x\neq -\frac{1}{2}\\a\in \mathrm{R}\text{, }&y=-\frac{5}{3}\text{ and }x=-\frac{1}{2}\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{-3y+a-5}{2a}\text{, }&a\neq 0\\x\in \mathrm{R}\text{, }&y=-\frac{5}{3}\text{ and }a=0\end{matrix}\right.
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2ax+a-5=3y
Swap sides so that all variable terms are on the left hand side.
2ax+a=3y+5
Add 5 to both sides.
\left(2x+1\right)a=3y+5
Combine all terms containing a.
\frac{\left(2x+1\right)a}{2x+1}=\frac{3y+5}{2x+1}
Divide both sides by 2x+1.
a=\frac{3y+5}{2x+1}
Dividing by 2x+1 undoes the multiplication by 2x+1.
2ax+a-5=3y
Swap sides so that all variable terms are on the left hand side.
2ax-5=3y-a
Subtract a from both sides.
2ax=3y-a+5
Add 5 to both sides.
\frac{2ax}{2a}=\frac{3y-a+5}{2a}
Divide both sides by 2a.
x=\frac{3y-a+5}{2a}
Dividing by 2a undoes the multiplication by 2a.
2ax+a-5=3y
Swap sides so that all variable terms are on the left hand side.
2ax+a=3y+5
Add 5 to both sides.
\left(2x+1\right)a=3y+5
Combine all terms containing a.
\frac{\left(2x+1\right)a}{2x+1}=\frac{3y+5}{2x+1}
Divide both sides by 2x+1.
a=\frac{3y+5}{2x+1}
Dividing by 2x+1 undoes the multiplication by 2x+1.
2ax+a-5=3y
Swap sides so that all variable terms are on the left hand side.
2ax-5=3y-a
Subtract a from both sides.
2ax=3y-a+5
Add 5 to both sides.
\frac{2ax}{2a}=\frac{3y-a+5}{2a}
Divide both sides by 2a.
x=\frac{3y-a+5}{2a}
Dividing by 2a undoes the multiplication by 2a.
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}