Solve {l}{y=x^2-x+1}{x=13/9}

$$\left\{ \begin{array} { l } { y = x ^ { 2 } - x + 1 } \\ { x = \frac { 13 } { 9 } } \end{array} \right.$$

Solve for y, x

$$x = \frac{13}{9} = 1\frac{4}{9} \approx 1.444444444$$

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

Solution Steps

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

$$y=\left(\frac{13}{9}\right)^{2}-\frac{13}{9}+1$$

Calculate \frac{13}{9} to the power of 2 and get \frac{169}{81}.

$$y=\frac{169}{81}-\frac{13}{9}+1$$

Subtract \frac{13}{9} from \frac{169}{81} to get \frac{52}{81}.

$$y=\frac{52}{81}+1$$

Add \frac{52}{81} and 1 to get \frac{133}{81}.

$$y=\frac{133}{81}$$

The system is now solved.

$$y=\frac{133}{81} x=\frac{13}{9}$$