Solve {l}{x-1=0}{text{Solvefor}y,ztext{where}}{y=x^5-x^4}{z=x^3-x^2}

$$\left. \begin{array} { l } { x - 1 = 0 }\\ { \text{Solve for } y,z \text{ where} } \\ { y = x ^ {5} - x ^ {4} }\\ { z = x ^ {3} - x ^ {2} } \end{array} \right.$$

Solve for x, y, z

$$y=0$$

$$z=0$$

Solution Steps

Consider the first equation. Add 1 to both sides. Anything plus zero gives itself.

$$x=1$$

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

$$y=1^{5}-1^{4}$$

Calculate 1 to the power of 5 and get 1.

$$y=1-1^{4}$$

Calculate 1 to the power of 4 and get 1.

$$y=1-1$$

Subtract 1 from 1 to get 0.

$$y=0$$

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

$$z=1^{3}-1^{2}$$

Calculate 1 to the power of 3 and get 1.

$$z=1-1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$z=1-1$$

Subtract 1 from 1 to get 0.

$$z=0$$

The system is now solved.

$$x=1 y=0 z=0$$