solve for X and Y
40/x+y + 2/x-y =5 and 
25 /x+y - 3/x-y =1 

Asked by shriya.pandey182 | 25th Jun, 2017, 06:14: PM

Expert Answer:

begin mathsize 16px style fraction numerator 40 over denominator straight x plus straight y end fraction plus fraction numerator begin display style 2 end style over denominator begin display style straight x minus straight y end style end fraction equals 5 space and space fraction numerator begin display style 25 end style over denominator begin display style straight x plus straight y end style end fraction minus fraction numerator begin display style 3 end style over denominator begin display style straight x minus straight y end style end fraction equals 1
Put space fraction numerator begin display style 1 end style over denominator begin display style straight x plus straight y end style end fraction equals straight u space space and space fraction numerator begin display style 1 end style over denominator begin display style straight x minus straight y end style end fraction equals straight v
40 straight u plus 2 straight v equals 5 space space space space.... left parenthesis straight i right parenthesis space
and space 25 straight u minus 3 straight v equals 1 space space space space space..... left parenthesis ii right parenthesis
Multiply space left parenthesis straight i right parenthesis space by space 3 space and space left parenthesis ii right parenthesis space by space 2 comma space we space get
120 straight u plus 6 straight v equals 15 space space space..... left parenthesis iii right parenthesis
and space 50 straight u minus 6 straight v equals 2 space space..... left parenthesis iv right parenthesis
Adding space left parenthesis iii right parenthesis space and space left parenthesis iv right parenthesis comma space we space get
170 straight u equals 17 rightwards double arrow straight u equals 1 over 10
Substituting space in space left parenthesis iv right parenthesis space to space get space the space value space of space straight v comma space we space get space straight v equals 1 half
So comma space fraction numerator begin display style 1 end style over denominator begin display style straight x plus straight y end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 10 end style end fraction space and space fraction numerator begin display style 1 end style over denominator begin display style straight x minus straight y end style end fraction equals fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction.
Thus comma space straight x plus straight y equals 10 space and space straight x minus straight y equals 2.
Adding space these space two space equations comma space we space get
2 straight x equals 12 rightwards double arrow straight x equals 6
Substituting space straight x equals 6 space in space straight x plus straight y equals 10 comma space we space get space straight y equals 4.
Hence comma space straight x equals 6 space and space straight y equals 4. end style

Answered by Rebecca | 26th Jun, 2017, 06:11: AM