Solve {l}{x=-3/2}{y=2x^4-5x^3-10x^2+15x+20}

$$\left\{ \begin{array} { l } { x = - \frac { 3 } { 2 } } \\ { y = 2 x ^ { 4 } - 5 x ^ { 3 } - 10 x ^ { 2 } + 15 x + 20 } \end{array} \right.$$

Solve for x, y

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

$$y=2$$

Solution Steps

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

$$y=2\left(-\frac{3}{2}\right)^{4}-5\left(-\frac{3}{2}\right)^{3}-10\left(-\frac{3}{2}\right)^{2}+15\left(-\frac{3}{2}\right)+20$$

Calculate -\frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$y=2\times \frac{81}{16}-5\left(-\frac{3}{2}\right)^{3}-10\left(-\frac{3}{2}\right)^{2}+15\left(-\frac{3}{2}\right)+20$$

Multiply 2 and \frac{81}{16} to get \frac{81}{8}.

$$y=\frac{81}{8}-5\left(-\frac{3}{2}\right)^{3}-10\left(-\frac{3}{2}\right)^{2}+15\left(-\frac{3}{2}\right)+20$$

Calculate -\frac{3}{2} to the power of 3 and get -\frac{27}{8}.

$$y=\frac{81}{8}-5\left(-\frac{27}{8}\right)-10\left(-\frac{3}{2}\right)^{2}+15\left(-\frac{3}{2}\right)+20$$

Multiply -5 and -\frac{27}{8} to get \frac{135}{8}.

$$y=\frac{81}{8}+\frac{135}{8}-10\left(-\frac{3}{2}\right)^{2}+15\left(-\frac{3}{2}\right)+20$$

Add \frac{81}{8} and \frac{135}{8} to get 27.

$$y=27-10\left(-\frac{3}{2}\right)^{2}+15\left(-\frac{3}{2}\right)+20$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$y=27-10\times \frac{9}{4}+15\left(-\frac{3}{2}\right)+20$$

Multiply -10 and \frac{9}{4} to get -\frac{45}{2}.

$$y=27-\frac{45}{2}+15\left(-\frac{3}{2}\right)+20$$

Subtract \frac{45}{2} from 27 to get \frac{9}{2}.

$$y=\frac{9}{2}+15\left(-\frac{3}{2}\right)+20$$

Multiply 15 and -\frac{3}{2} to get -\frac{45}{2}.

$$y=\frac{9}{2}-\frac{45}{2}+20$$

Subtract \frac{45}{2} from \frac{9}{2} to get -18.

$$y=-18+20$$

Add -18 and 20 to get 2.

$$y=2$$

The system is now solved.

$$x=-\frac{3}{2} y=2$$