Question

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`(a)/(b) - (b)/(2) = 10 \\ a - b = 29`
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Answer 1

(8.21, -20.79)

Explanation:

Given the simultaneous equation;

`(a)/(b) - (b)/(2) = 10\\a - b = 29`

From 2;

a = 29 + b ....3

Substitute 3 into 1;

`(29+b)/(b) - (b)/(2) = 10\\(2(29+b)-b^2)/(2b) = 10\\(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\\`

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)