Solve ax^2-1/y=5

$$\frac { a x ^ { 2 } - 1 } { y } = 5$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{5y+1}{x^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\\a\in \mathrm{C}\text{, }&x=0\text{ and }y=-\frac{1}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$ax^{2}-1=5y$$

Add 1 to both sides.

$$ax^{2}=5y+1$$

The equation is in standard form.

$$x^{2}a=5y+1$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{5y+1}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{5y+1}{x^{2}}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{5y+1}{x^{2}}\text{, }&x\neq 0\text{ and }y\neq 0\\a\in \mathrm{R}\text{, }&x=0\text{ and }y=-\frac{1}{5}\end{matrix}\right.$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$ax^{2}-1=5y$$

Add 1 to both sides.

$$ax^{2}=5y+1$$

The equation is in standard form.

$$x^{2}a=5y+1$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=\frac{5y+1}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=\frac{5y+1}{x^{2}}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-a^{-\frac{1}{2}}\sqrt{5y+1}\text{; }x=a^{-\frac{1}{2}}\sqrt{5y+1}\text{, }&a\neq 0\text{ and }y\neq 0\\x\in \mathrm{C}\text{, }&a=0\text{ and }y=-\frac{1}{5}\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\sqrt{\frac{5y+1}{a}}\text{; }x=-\sqrt{\frac{5y+1}{a}}\text{, }&\left(y\leq -\frac{1}{5}\text{ and }a<0\right)\text{ or }\left(y\geq -\frac{1}{5}\text{ and }a>0\text{ and }y\neq 0\right)\\x\in \mathrm{R}\text{, }&a=0\text{ and }y=-\frac{1}{5}\end{matrix}\right.$$