# System of Equations...3

Discussion in 'Other Pre-University Math' started by nycmathguy, Nov 1, 2021.

1. ### nycmathguy

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nycmathguy, Nov 1, 2021

2. ### MathLover1

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where did you find that one?
solutions are a bit complicated, you have two equations and four unknown variables
it takes a lot to get solutions of two variables expressed in terms of two other variables

solution looks like this:

or

Last edited: Nov 1, 2021
MathLover1, Nov 1, 2021
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3. ### nycmathguy

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All the system of equations threads come from David Cohen's Precalculus With Unit Circle Trigonometry Edition 4 textbook.

Instructions:

Solve each system of equations. If
there are no solutions in a particular case, say so. In cases in which there are literal (rather than numerical) coefficients, specify any restrictions that your solutions impose on those coefficients.

nycmathguy, Nov 1, 2021
4. ### MathLover1

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(2b)/x-3/y=7ab..........eq.1
(4a)/x-(5a)/(by)=3a^2......eq.2
---------------------------------------

(2b)/x-3/y=7ab..........eq.1, solve for x

(2b)/x=7ab+3/y

x=(2b)/(7ab+3/y)............eq.1a

substitute x in eq.2
(4a)/((2b)/(7ab+3/y))-(5a)/(by)=3a^2......eq.2, solve for y

14a^2 + (6a)/(by)-(5a)/(by)=3a^2
(6a)/(by)-(5a)/(by)=3a^2-14a^2
(6a-5a)/(by)=-11a^2
a/(by)=-11a^2
a/(-11a^2)= by
-1/(11a)= by

y=-1/(11ab)

go to
x=(2b)/(7ab+3/y)............eq.1a, substitute y

x=(2b)/(7ab+3/(-1/(11ab)))
x=(2b)/(7ab-3(11ab))
x=(2b)/(7ab-33ab)
x=(2b)/(-26ab)
x=-1/(13a)

restrictions:

MathLover1, Nov 1, 2021
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