Solve and find x and y:-

1/2(x+2y) +5/4(3x-2y)=-3/2 -------(i)

5/4(x+2y) - 3/5(3x-2y)=61/60 ---------(ii)

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Solution

1 / 2(x +2y) +5 / 3(3x-2y) = 3/2, 5/4(x+2y) - 3/5(3x-2y) = 61/60
Let (x +2y) = a and (3x-2y) = b then
1 / 2a + 5 / 3b = 3/2 5 / 4a - 3 / 5b = 61 / 60
10a + 3b = -9ab ,--------(1) -36a + 75b =61ab --------(2)
substract 25 x (1) - (2) we get b = -1
adding 18x (1) + 5 x (2) we get a = 3
subsitute a,b values then
(x +2y) = 3 --------(3) and (3x-2y) = -1 --------(4)
silving (3) and (4)
we get x = 1/2 , y = 5/4.

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Similar questions

x \neq 0, y \neq 0 :

\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2} \frac{5}{4 (x + 2 y)} - \frac{3}{5 (3 x - 2 y)} = \frac{61}{60}

Solve for x and y:

$\frac{1}{2 (3 x + y)} + \frac{5}{3 (3 x - y)} = \frac{- 3}{2} \frac{5}{4 (x + 2 y)} - \frac{3}{5 (3 x - 2 y)} = \frac{61}{60} .$

\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2}

\frac{5}{4 (x + 2 y)} - \frac{3}{5 (3 x - 2 y)} = \frac{61}{60}

Solve the following systems of equations:

$\frac{1}{2 (x + 2 y)} + \frac{5}{3 (3 x - 2 y)} = \frac{- 3}{2}$

$\frac{5}{4 (x + 2 y)} - \frac{5}{5 (3 x - 2 y)} = \frac{61}{60}$

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