Solve {l}{g{(x)}={(1/4)}^3-3}{h=g{(5)}}{i=h}{j=i}{text{Solvefor}ktext{where}}{k=j}

$$\left. \begin{array} { l } { g {(x)} = {(\frac{1}{4})} ^ {3} - 3 }\\ { h = g {(5)} }\\ { i = h }\\ { j = i }\\ { \text{Solve for } k \text{ where} } \\ { k = j } \end{array} \right.$$

Solve for g, x, h, j, k

$$k=i$$

Solution Steps

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

$$h=i$$

Consider the second equation. Insert the known values of variables into the equation.

$$i=g\times 5$$

Divide both sides by 5.

$$\frac{i}{5}=g$$

Divide i by 5 to get \frac{1}{5}i.

$$\frac{1}{5}i=g$$

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

$$g=\frac{1}{5}i$$

Consider the first equation. Insert the known values of variables into the equation.

$$\frac{1}{5}ix=\left(\frac{1}{4}\right)^{3}-3$$

Calculate \frac{1}{4} to the power of 3 and get \frac{1}{64}.

$$\frac{1}{5}ix=\frac{1}{64}-3$$

Subtract 3 from \frac{1}{64} to get -\frac{191}{64}.

$$\frac{1}{5}ix=-\frac{191}{64}$$

Divide both sides by \frac{1}{5}i.

$$x=\frac{-\frac{191}{64}}{\frac{1}{5}i}$$

Multiply both numerator and denominator of \frac{-\frac{191}{64}}{\frac{1}{5}i} by imaginary unit i.

$$x=\frac{-\frac{191}{64}i}{-\frac{1}{5}}$$

Divide -\frac{191}{64}i by -\frac{1}{5} to get \frac{955}{64}i.

$$x=\frac{955}{64}i$$

The system is now solved.

$$g=\frac{1}{5}i x=\frac{955}{64}i h=i j=i k=i$$