Solve {l}{1/2ah=1/2{(a+2)}}{i={(h-3)}}{text{Solvefor}jtext{where}}{j=i}

$$\left. \begin{array} { l } { \frac{1}{2} a h = \frac{1}{2} {(a + 2)} }\\ { i = {(h - 3)} }\\ { \text{Solve for } j \text{ where} } \\ { j = i } \end{array} \right.$$

Solve for a, h, j

$$j=i$$

Short Steps Using Substitution

Reorder the equations.

$$i=h-3 \frac{1}{2}ah=\frac{1}{2}\left(a+2\right) j=i$$

Solve i=h-3 for h.

$$h=3+i$$

Substitute 3+i for h in the equation \frac{1}{2}ah=\frac{1}{2}\left(a+2\right).

$$\frac{1}{2}a\left(3+i\right)=\frac{1}{2}\left(a+2\right)$$

Solve \frac{1}{2}a\left(3+i\right)=\frac{1}{2}\left(a+2\right) for a.

$$a=\frac{4}{5}-\frac{2}{5}i$$

The system is now solved.

$$a=\frac{4}{5}-\frac{2}{5}i h=3+i j=i$$