Solve {l}{11x-6=0}{text{Solvefor}ytext{where}}{y=x^3-6x^2}

$$\left. \begin{array} { l } { 11 x - 6 = 0 }\\ { \text{Solve for } y \text{ where} } \\ { y = x ^ {3} - 6 x ^ {2} } \end{array} \right.$$

Solve for x, y

$$y = -\frac{2160}{1331} = -1\frac{829}{1331} \approx -1.62283997$$

Solution Steps

Consider the first equation. Add 6 to both sides. Anything plus zero gives itself.

$$11x=6$$

Divide both sides by 11.

$$x=\frac{6}{11}$$

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

$$y=\left(\frac{6}{11}\right)^{3}-6\times \left(\frac{6}{11}\right)^{2}$$

Calculate \frac{6}{11} to the power of 3 and get \frac{216}{1331}.

$$y=\frac{216}{1331}-6\times \left(\frac{6}{11}\right)^{2}$$

Calculate \frac{6}{11} to the power of 2 and get \frac{36}{121}.

$$y=\frac{216}{1331}-6\times \frac{36}{121}$$

Multiply -6 and \frac{36}{121} to get -\frac{216}{121}.

$$y=\frac{216}{1331}-\frac{216}{121}$$

Subtract \frac{216}{121} from \frac{216}{1331} to get -\frac{2160}{1331}.

$$y=-\frac{2160}{1331}$$

The system is now solved.

$$x=\frac{6}{11} y=-\frac{2160}{1331}$$