Solve {l}{S=-3/2m^2+9/2m+9/2}{m=3/2}

$$\left\{ \begin{array} { l } { S = - \frac { 3 } { 2 } m ^ { 2 } + \frac { 9 } { 2 } m + \frac { 9 } { 2 } } \\ { m = \frac { 3 } { 2 } } \end{array} \right.$$

Solve for S, m

$$S = \frac{63}{8} = 7\frac{7}{8} = 7.875$$

$$m = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Solution Steps

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

$$S=-\frac{3}{2}\times \left(\frac{3}{2}\right)^{2}+\frac{9}{2}\times \frac{3}{2}+\frac{9}{2}$$

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

$$S=-\frac{3}{2}\times \frac{9}{4}+\frac{9}{2}\times \frac{3}{2}+\frac{9}{2}$$

Multiply -\frac{3}{2} and \frac{9}{4} to get -\frac{27}{8}.

$$S=-\frac{27}{8}+\frac{9}{2}\times \frac{3}{2}+\frac{9}{2}$$

Multiply \frac{9}{2} and \frac{3}{2} to get \frac{27}{4}.

$$S=-\frac{27}{8}+\frac{27}{4}+\frac{9}{2}$$

Add -\frac{27}{8} and \frac{27}{4} to get \frac{27}{8}.

$$S=\frac{27}{8}+\frac{9}{2}$$

Add \frac{27}{8} and \frac{9}{2} to get \frac{63}{8}.

$$S=\frac{63}{8}$$

The system is now solved.

$$S=\frac{63}{8} m=\frac{3}{2}$$