Solve {l}{x+1=0}{text{Solvefor}ytext{where}}{y=x^4+x^3+x^2+x}

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

Solve for x, y

$$y=0$$

Solution Steps

Consider the first equation. Subtract 1 from both sides. Anything subtracted from zero gives its negation.

$$x=-1$$

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

$$y=\left(-1\right)^{4}+\left(-1\right)^{3}+\left(-1\right)^{2}-1$$

Calculate -1 to the power of 4 and get 1.

$$y=1+\left(-1\right)^{3}+\left(-1\right)^{2}-1$$

Calculate -1 to the power of 3 and get -1.

$$y=1-1+\left(-1\right)^{2}-1$$

Subtract 1 from 1 to get 0.

$$y=\left(-1\right)^{2}-1$$

Calculate -1 to the power of 2 and get 1.

$$y=1-1$$

Subtract 1 from 1 to get 0.

$$y=0$$

The system is now solved.

$$x=-1 y=0$$