Solve y=operatornametag^-1(5/-6)

$$y = \operatorname { tag } ^ { - 1 } ( \frac { 5 } { - 6 } )$$

Solve for a

$$a=-\frac{5}{6gty}$$

$$t\neq 0\text{ and }g\neq 0\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Expand \left(tag\right)^{-1}.

$$y=t^{-1}a^{-1}g^{-1}\times \frac{5}{-6}$$

Fraction \frac{5}{-6} can be rewritten as -\frac{5}{6} by extracting the negative sign.

$$y=t^{-1}a^{-1}g^{-1}\left(-\frac{5}{6}\right)$$

Swap sides so that all variable terms are on the left hand side.

$$t^{-1}a^{-1}g^{-1}\left(-\frac{5}{6}\right)=y$$

Reorder the terms.

$$-\frac{5}{6}\times \frac{1}{a}\times \frac{1}{g}\times \frac{1}{t}=y$$

Variable a cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 6agt, the least common multiple of 6,a,g,t.

$$-\frac{5}{6}\times 6gt\times \frac{1}{g}\times \frac{1}{t}=y\times 6agt$$

Multiply -\frac{5}{6} and 6 to get -5.

$$-5gt\times \frac{1}{g}\times \frac{1}{t}=y\times 6agt$$

Express -5\times \frac{1}{g} as a single fraction.

$$\frac{-5}{g}gt\times \frac{1}{t}=y\times 6agt$$

Multiply \frac{-5}{g} times \frac{1}{t} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-5}{gt}gt=y\times 6agt$$

Express \frac{-5}{gt}g as a single fraction.

$$\frac{-5g}{gt}t=y\times 6agt$$

Cancel out g in both numerator and denominator.

$$\frac{-5}{t}t=y\times 6agt$$

Express \frac{-5}{t}t as a single fraction.

$$\frac{-5t}{t}=y\times 6agt$$

Cancel out t in both numerator and denominator.

$$-5=y\times 6agt$$

Swap sides so that all variable terms are on the left hand side.

$$y\times 6agt=-5$$

The equation is in standard form.

$$6gtya=-5$$

Divide both sides by 6ygt.

$$\frac{6gtya}{6gty}=-\frac{5}{6gty}$$

Dividing by 6ygt undoes the multiplication by 6ygt.

$$a=-\frac{5}{6gty}$$

Variable a cannot be equal to 0.

$$a=-\frac{5}{6gty}\text{, }a\neq 0$$

Solve for g

$$g=-\frac{5}{6aty}$$

$$t\neq 0\text{ and }a\neq 0\text{ and }y\neq 0$$