Solve {l}{-3x-8=0}{text{Solvefor}ytext{where}}{y=2x^3-28x^2}

$$\left. \begin{array} { l } { -3 x - 8 = 0 }\\ { \text{Solve for } y \text{ where} } \\ { y = 2 x ^ {3} - 28 x ^ {2} } \end{array} \right.$$

Solve for x, y

$$y = -\frac{6400}{27} = -237\frac{1}{27} \approx -237.037037037$$

Solution Steps

Consider the first equation. Add 8 to both sides. Anything plus zero gives itself.

$$-3x=8$$

Divide both sides by -3.

$$x=-\frac{8}{3}$$

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

$$y=2\left(-\frac{8}{3}\right)^{3}-28\left(-\frac{8}{3}\right)^{2}$$

Calculate -\frac{8}{3} to the power of 3 and get -\frac{512}{27}.

$$y=2\left(-\frac{512}{27}\right)-28\left(-\frac{8}{3}\right)^{2}$$

Multiply 2 and -\frac{512}{27} to get -\frac{1024}{27}.

$$y=-\frac{1024}{27}-28\left(-\frac{8}{3}\right)^{2}$$

Calculate -\frac{8}{3} to the power of 2 and get \frac{64}{9}.

$$y=-\frac{1024}{27}-28\times \frac{64}{9}$$

Multiply -28 and \frac{64}{9} to get -\frac{1792}{9}.

$$y=-\frac{1024}{27}-\frac{1792}{9}$$

Subtract \frac{1792}{9} from -\frac{1024}{27} to get -\frac{6400}{27}.

$$y=-\frac{6400}{27}$$

The system is now solved.

$$x=-\frac{8}{3} y=-\frac{6400}{27}$$