Solve for a (complex solution)
\left\{\begin{matrix}a=-\frac{2y-x}{x+y-3}\text{, }&x\neq 3-y\\a\in \mathrm{C}\text{, }&x=2\text{ and }y=1\end{matrix}\right.
Solve for x (complex solution)
\left\{\begin{matrix}x=-\frac{ay+2y-3a}{a-1}\text{, }&a\neq 1\\x\in \mathrm{C}\text{, }&y=1\text{ and }a=1\end{matrix}\right.
Solve for a
\left\{\begin{matrix}a=-\frac{2y-x}{x+y-3}\text{, }&x\neq 3-y\\a\in \mathrm{R}\text{, }&x=2\text{ and }y=1\end{matrix}\right.
Solve for x
\left\{\begin{matrix}x=-\frac{ay+2y-3a}{a-1}\text{, }&a\neq 1\\x\in \mathrm{R}\text{, }&y=1\text{ and }a=1\end{matrix}\right.
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ax-x+\left(a+2\right)y=3a
Use the distributive property to multiply a-1 by x.
ax-x+ay+2y=3a
Use the distributive property to multiply a+2 by y.
ax-x+ay+2y-3a=0
Subtract 3a from both sides.
ax+ay+2y-3a=x
Add x to both sides. Anything plus zero gives itself.
ax+ay-3a=x-2y
Subtract 2y from both sides.
\left(x+y-3\right)a=x-2y
Combine all terms containing a.
\frac{\left(x+y-3\right)a}{x+y-3}=\frac{x-2y}{x+y-3}
Divide both sides by x+y-3.
a=\frac{x-2y}{x+y-3}
Dividing by x+y-3 undoes the multiplication by x+y-3.
ax-x+\left(a+2\right)y=3a
Use the distributive property to multiply a-1 by x.
ax-x+ay+2y=3a
Use the distributive property to multiply a+2 by y.
ax-x+2y=3a-ay
Subtract ay from both sides.
ax-x=3a-ay-2y
Subtract 2y from both sides.
\left(a-1\right)x=3a-ay-2y
Combine all terms containing x.
\left(a-1\right)x=3a-2y-ay
The equation is in standard form.
\frac{\left(a-1\right)x}{a-1}=\frac{3a-2y-ay}{a-1}
Divide both sides by a-1.
x=\frac{3a-2y-ay}{a-1}
Dividing by a-1 undoes the multiplication by a-1.
ax-x+\left(a+2\right)y=3a
Use the distributive property to multiply a-1 by x.
ax-x+ay+2y=3a
Use the distributive property to multiply a+2 by y.
ax-x+ay+2y-3a=0
Subtract 3a from both sides.
ax+ay+2y-3a=x
Add x to both sides. Anything plus zero gives itself.
ax+ay-3a=x-2y
Subtract 2y from both sides.
\left(x+y-3\right)a=x-2y
Combine all terms containing a.
\frac{\left(x+y-3\right)a}{x+y-3}=\frac{x-2y}{x+y-3}
Divide both sides by x+y-3.
a=\frac{x-2y}{x+y-3}
Dividing by x+y-3 undoes the multiplication by x+y-3.
ax-x+\left(a+2\right)y=3a
Use the distributive property to multiply a-1 by x.
ax-x+ay+2y=3a
Use the distributive property to multiply a+2 by y.
ax-x+2y=3a-ay
Subtract ay from both sides.
ax-x=3a-ay-2y
Subtract 2y from both sides.
\left(a-1\right)x=3a-ay-2y
Combine all terms containing x.
\left(a-1\right)x=3a-2y-ay
The equation is in standard form.
\frac{\left(a-1\right)x}{a-1}=\frac{3a-2y-ay}{a-1}
Divide both sides by a-1.
x=\frac{3a-2y-ay}{a-1}
Dividing by a-1 undoes the multiplication by a-1.
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}