Question

Solve for x and y6/x+2y + 5/x-2y = -3 ;3/x+2y + 7/x-2y = -6​

Answer 1

Step-by-step explanation:

Let

{1/(x+2y)} = u -----Eqn(1)

{1/(x-2y)} = v ------Eqn(2)

So, given equation can be rewritten as

⇛6u + 5v = -3 ---Eqn(3)

⇛3u + 7v = -6 -----Eqn(4)

On multiply equation (4) by 2, we get

⇛6u + 14v = -12 -----Eqn(5)

On subtracting equation (3) from equation (5), we get

⇛9v = -9

⇛v = -9/9

⇛v = -1 ----Eqn(6)

Put value of v in equation (3), we get

6u + 5v = -3

⇛6u + 5 * (-1) = -3

⇛6u -5 = -3

⇛6u = -3 + 5

⇛6u = 2

⇛u = 2/6

⇛u = (2÷2)/(6÷2)

⇛u = 1/3 -----Eqn(7)

Now, substituting value of u and v in equation (1) and equation (2), we get

{1/(x+2y)} = 1/3 and {1/(x-2y)} = -1

⇛x + 2y = 3 -----Eqn(8)

⇛x - 2y = -1 -------Eqn(9)

Now, add equation (8) and equation (9) , we get

⇛2x = 2

⇛x = 2/2

⇛x = 1 -----Eqn(10)

On substituting x = 1 in equation (8), we get

x + 2y = 3

⇛ 1 + 2y = 3

⇛2y = 3 - 1

⇛2y = 2

⇛y = 2/2

⇛y = 1 ------Eqn(11)

Therefore, x = 1 and y = 1

Answer: Hence the value of x and y is 1 and 1.