By solving the simultaneous equations \(\rm\frac{2}{x}+\frac{3}{y}\) = 7 and \(\rm\frac{1}{x}−\frac{4}{y}\) = −2, solution obtained for (x, y) is

Explanation:

Firstly, let's re-write the equations in terms of x and y. You have two equations:

2/x + 3/y = 7
1/x - 4/y = -2

To make the calculations easier, we'll multiply each term by xy to get rid of the fractions:

2y + 3x = 7xy ---- (equation 1)
y - 4x = -2xy ---- (equation 2)

Now, let's solve these equations step by step.

Multiply equation 2 by 2:

2y - 8x = -4xy

Now, subtract this result from equation 1:

2y + 3x - 2y + 8x = 7xy - (-4xy)

11x = 11xy

From here, we can conclude that either x = 0, or y = 1. Since x = 0 doesn't make sense in the context of our original equations (it would require dividing by zero), we conclude that y = 1.

Substitute y = 1 into equation 2:

1 - 4x = -2x

-4x + 2x = -1

-2x = -1

x = 1/2

so, the correct answer is option 1.