Solve {l}{b=a^2+2a-3}{a=-15/4}

$$\left\{ \begin{array} { l } { b = a ^ { 2 } + 2 a - 3 } \\ { a = - \frac { 15 } { 4 } } \end{array} \right.$$

Solve for b, a

$$b = \frac{57}{16} = 3\frac{9}{16} = 3.5625$$

$$a = -\frac{15}{4} = -3\frac{3}{4} = -3.75$$

Solution Steps

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

$$b=\left(-\frac{15}{4}\right)^{2}+2\left(-\frac{15}{4}\right)-3$$

Calculate -\frac{15}{4} to the power of 2 and get \frac{225}{16}.

$$b=\frac{225}{16}+2\left(-\frac{15}{4}\right)-3$$

Multiply 2 and -\frac{15}{4} to get -\frac{15}{2}.

$$b=\frac{225}{16}-\frac{15}{2}-3$$

Subtract \frac{15}{2} from \frac{225}{16} to get \frac{105}{16}.

$$b=\frac{105}{16}-3$$

Subtract 3 from \frac{105}{16} to get \frac{57}{16}.

$$b=\frac{57}{16}$$

The system is now solved.

$$b=\frac{57}{16} a=-\frac{15}{4}$$