Solve {l}{x=23/6}{y=-x^2+7/2x+2}

$$\left. \begin{array} { l } { x = \frac { 23 } { 6 } } \\ { y = - x ^ { 2 } + \frac { 7 } { 2 } x + 2 } \end{array} \right.$$

Solve for x, y

$$x = \frac{23}{6} = 3\frac{5}{6} \approx 3.833333333$$

$$y=\frac{13}{18}\approx 0.722222222$$

Solution Steps

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

$$y=-\left(\frac{23}{6}\right)^{2}+\frac{7}{2}\times \frac{23}{6}+2$$

Calculate \frac{23}{6} to the power of 2 and get \frac{529}{36}.

$$y=-\frac{529}{36}+\frac{7}{2}\times \frac{23}{6}+2$$

Multiply \frac{7}{2} and \frac{23}{6} to get \frac{161}{12}.

$$y=-\frac{529}{36}+\frac{161}{12}+2$$

Add -\frac{529}{36} and \frac{161}{12} to get -\frac{23}{18}.

$$y=-\frac{23}{18}+2$$

Add -\frac{23}{18} and 2 to get \frac{13}{18}.

$$y=\frac{13}{18}$$

The system is now solved.

$$x=\frac{23}{6} y=\frac{13}{18}$$