Solve {l}{y=x^2-x+1}{x=133/81}

$$\left\{ \begin{array} { l } { y = x ^ { 2 } - x + 1 } \\ { x = \frac { 133 } { 81 } } \end{array} \right.$$

Solve for y, x

$$x = \frac{133}{81} = 1\frac{52}{81} \approx 1.641975309$$

$$y = \frac{13477}{6561} = 2\frac{355}{6561} \approx 2.054107606$$

Solution Steps

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

$$y=\left(\frac{133}{81}\right)^{2}-\frac{133}{81}+1$$

Calculate \frac{133}{81} to the power of 2 and get \frac{17689}{6561}.

$$y=\frac{17689}{6561}-\frac{133}{81}+1$$

Subtract \frac{133}{81} from \frac{17689}{6561} to get \frac{6916}{6561}.

$$y=\frac{6916}{6561}+1$$

Add \frac{6916}{6561} and 1 to get \frac{13477}{6561}.

$$y=\frac{13477}{6561}$$

The system is now solved.

$$y=\frac{13477}{6561} x=\frac{133}{81}$$