Answer:
(8.21, -20.79)
Step-by-step explanation:
Given the simultaneous equation;
[tex]\frac{a}{b} - \frac{b}{2} = 10\\a - b = 29[/tex]
From 2;
a = 29 + b ....3
Substitute 3 into 1;
[tex]\frac{29+b}{b} - \frac{b}{2} = 10\\\frac{2(29+b)-b^2}{2b} = 10\\\frac{58+2b-b^2}{2b} = 10\\58+2b-b^2 = 20b\\b^2-2b-58 = -20b\\b^2-2b+20b -58 = 0\\b^2+18b-58 = 0\\[/tex]
Factorize
b = -18±√18²-4(-58)/2
b = -18±√324+232/2
b = -18±√556/2
b = -18±23.58/2
b = -18-23.58/2 and -18+23.58/2
b = -41.58/2 and 5.58/2
b = -20.79 and 2.79
Since a = 29 + b
when b = -20.79
a = 29 - 20.79
a = 8.21
Hence the solution to the system of equation is (8.21, -20.79)
