Question

find x and y using subtitution method 1/2(x+2y) + 5/3(3x-2y)= 3/2 and 5/4(x+2y) - 3/5(3x-2y)=61/60

Answer 1

x-2y)] = -3/2, 5 / [4(x+2y)] - 3 / [5(3x-2y)] = 61/60

Let  1/(x+2y) = a ,  1 / (3x-2y) = b then

a / 2 + 5b / 3 = -3 / 2  and   5a /4 - 3b / 5 = 61 /60
⇒ (3a +10b) / 3 = -3  and 25a - 12b = 61 / 3
⇒ (3a +10b)  = -9  -------------(1)  and 75a - 36b = 61  -------------------(2)
multiply euation (1) by 25 and substract from to euation (2) we get 'b' value .
And b value subsitute in any one equations 1 & 2 we get 'a' value
Again subsisitute a,b values in above euations  and solve it we get x and y values

Answer 2

Given 1 / [2(x+2y)] + 5 / [3(3x-2y)] = -3/2, 5 / [4(x+2y)] - 3 / [5(3x-2y)] = 61/60

Let  1/(x+2y) = a ,  1 / (3x-2y) = b then

a / 2 + 5b / 3 = -3 / 2  and   5a /4 - 3b / 5 = 61 /60
⇒ (3a +10b) / 3 = -3  and 25a - 12b = 61 / 3
⇒ (3a +10b)  = -9  -------------(1)  and 75a - 36b = 61  -------------------(2)
multiply euation (1) by 25 and substract from to euation (2) we get 'b' value .
And b value subsitute in any one equations 1 & 2 we get 'a' value
Again subsisitute a,b values in above euations  and solve it we get x and y values.