Consider this system of equations:

\(^2/_3x+\text{ }^3/_5y=12\) (equation A)

\(^5/_2y-3x=6\)(equation B)

The expression that gives the value of x is \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\).
The solution for the system of equations is \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\).


\(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\\ \boxed{^{5a}/_3+\text{ }^{2b}/_5\text{ }\text{ }\text{ }\text{ }\text{ }\\\ ^{3a}/_5-\text{ }^{5b}/_2\\ ^{5a}/_2+\text{ }^{3b}/_5\\ ^{5a}/_3-\text{ }^{2b}/_5\\ ^{3a}/_2+\text{ }^b/_5}\) \(\boxed{\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\downarrow}\\ \boxed{(^{1118}/_{47},\text{ }^{396}/_{47})\text{ }\text{ }\text{ }\\ (^{33}/_{13},\text{ }^{50}/_{13})\\ (^{99}/_{13},\text{ }^{150}/_{13})\\ (8,12)}\)

SpaceModo  Jan 24, 2018
edited by SpaceModo  Jan 24, 2018

(2/3)x  + (3/5)y  =  12

-3x   + (5/2)y  =  6


Mutiply  the first equation through by the common denominator of 3 and 5 = 15

Multiply the second equation through by 2


So we have


10x  +  9y   =  180    multipy through by 6  =   60x + 54y  = 1080    (1)

-6x  +  5y      =  12  multiply through   by 10  =   -60x  + 50y  =   120    (2)


Add (1)  and (2)


104y  =  1200     divide by  104


y =   1200/104 =   600/52  =  150 / 13


Obviously, only one answer has a "y" answer that  =  150/13.....so that must be the correct one



cool cool cool

CPhill  Jan 24, 2018

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