Solve {l}{y=1-0.2(x/13)-0.8(x/13)^2}{x=10.6}

$$\left. \begin{array} { l } { y = 1 - 0.2 ( \frac { x } { 13 } ) - 0.8 ( \frac { x } { 13 } ) ^ { 2 } } \\ { x = 10.6 } \end{array} \right.$$

Solve for y, x

$$x=10.6$$

$$y=\frac{6444}{21125}\approx 0.30504142$$

Solution Steps

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

$$y=1-0.2\times \frac{10.6}{13}-0.8\times \left(\frac{10.6}{13}\right)^{2}$$

Expand \frac{10.6}{13} by multiplying both numerator and the denominator by 10.

$$y=1-0.2\times \frac{106}{130}-0.8\times \left(\frac{10.6}{13}\right)^{2}$$

Reduce the fraction \frac{106}{130} to lowest terms by extracting and canceling out 2.

$$y=1-0.2\times \frac{53}{65}-0.8\times \left(\frac{10.6}{13}\right)^{2}$$

Multiply 0.2 and \frac{53}{65} to get \frac{53}{325}.

$$y=1-\frac{53}{325}-0.8\times \left(\frac{10.6}{13}\right)^{2}$$

Subtract \frac{53}{325} from 1 to get \frac{272}{325}.

$$y=\frac{272}{325}-0.8\times \left(\frac{10.6}{13}\right)^{2}$$

Expand \frac{10.6}{13} by multiplying both numerator and the denominator by 10.

$$y=\frac{272}{325}-0.8\times \left(\frac{106}{130}\right)^{2}$$

Reduce the fraction \frac{106}{130} to lowest terms by extracting and canceling out 2.

$$y=\frac{272}{325}-0.8\times \left(\frac{53}{65}\right)^{2}$$

Calculate \frac{53}{65} to the power of 2 and get \frac{2809}{4225}.

$$y=\frac{272}{325}-0.8\times \frac{2809}{4225}$$

Multiply 0.8 and \frac{2809}{4225} to get \frac{11236}{21125}.

$$y=\frac{272}{325}-\frac{11236}{21125}$$

Subtract \frac{11236}{21125} from \frac{272}{325} to get \frac{6444}{21125}.

$$y=\frac{6444}{21125}$$

The system is now solved.

$$y=\frac{6444}{21125} x=10.6$$