$$15(a-4)-2(a-9)+5(a+b)=0$$
$a=-\frac{5b}{18}+\frac{7}{3}$
$$15a-60-2\left(a-9\right)+5\left(a+b\right)=0$$
$$15a-60-2a+18+5\left(a+b\right)=0$$
$$13a-60+18+5\left(a+b\right)=0$$
$$13a-42+5\left(a+b\right)=0$$
$$13a-42+5a+5b=0$$
$$18a-42+5b=0$$
$$18a+5b=42$$
$$18a=42-5b$$
$$\frac{18a}{18}=\frac{42-5b}{18}$$
$$a=\frac{42-5b}{18}$$
$$a=-\frac{5b}{18}+\frac{7}{3}$$
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$b=\frac{42-18a}{5}$
$$-42+5b=-18a$$
$$5b=-18a+42$$
$$5b=42-18a$$
$$\frac{5b}{5}=\frac{42-18a}{5}$$
$$b=\frac{42-18a}{5}$$
