Solve {l}{22-2(h+2)-3(h-1)=h+3}{4[4-5(3j-2)]=92-5i}

$$\left. \begin{array} { l } { 22 - 2 ( h + 2 ) - 3 ( h - 1 ) = h + 3 } \\ { 4 [ 4 - 5 ( 3 j - 2 ) ] = 92 - 5 i } \end{array} \right.$$

Solve for h, j

$$h=3$$

$$j=-\frac{3}{5}+\frac{1}{12}i\approx -0.6+0.083333333i$$

Solution Steps

Consider the first equation. Use the distributive property to multiply -2 by h+2.

$$22-2h-4-3\left(h-1\right)=h+3$$

Subtract 4 from 22 to get 18.

$$18-2h-3\left(h-1\right)=h+3$$

Use the distributive property to multiply -3 by h-1.

$$18-2h-3h+3=h+3$$

Combine -2h and -3h to get -5h.

$$18-5h+3=h+3$$

Add 18 and 3 to get 21.

$$21-5h=h+3$$

Subtract h from both sides.

$$21-5h-h=3$$

Combine -5h and -h to get -6h.

$$21-6h=3$$

Subtract 21 from both sides.

$$-6h=3-21$$

Subtract 21 from 3 to get -18.

$$-6h=-18$$

Divide both sides by -6.

$$h=\frac{-18}{-6}$$

Divide -18 by -6 to get 3.

$$h=3$$

Consider the second equation. Divide both sides by 4.

$$4-5\left(3j-2\right)=\frac{92-5i}{4}$$

Divide 92-5i by 4 to get 23-\frac{5}{4}i.

$$4-5\left(3j-2\right)=23-\frac{5}{4}i$$

Use the distributive property to multiply -5 by 3j-2.

$$4-15j+10=23-\frac{5}{4}i$$

Add 4 and 10 to get 14.

$$14-15j=23-\frac{5}{4}i$$

Subtract 14 from both sides.

$$-15j=23-\frac{5}{4}i-14$$

Subtract 14 from 23-\frac{5}{4}i to get 9-\frac{5}{4}i.

$$-15j=9-\frac{5}{4}i$$

Divide both sides by -15.

$$j=\frac{9-\frac{5}{4}i}{-15}$$

Divide 9-\frac{5}{4}i by -15 to get -\frac{3}{5}+\frac{1}{12}i.

$$j=-\frac{3}{5}+\frac{1}{12}i$$

The system is now solved.

$$h=3 j=-\frac{3}{5}+\frac{1}{12}i$$