Question

1/x+1/y=7/12,1/x-1/y=1/12

Answer 1

Ответ:

Объяснение:

1/х+1/у=7/12    

х+у/ху=7/12    

12(х+у)=7 ху

12х+12у=7ху

х(12-7у)=-12у

х=-12у/12-7у

Answer 2

To solve the system of equations:

1. 1/x + 1/y = 7/12
2. 1/x - 1/y = 1/12

Let's first eliminate one of the variables, say y. We can do this by adding the two equations together, which will cancel out the terms with y:

(1) + (2): (1/x + 1/y) + (1/x - 1/y) = 7/12 + 1/12

Simplifying the left side: 2/x = 8/12

Now, let's solve for x: 2/x = 2/3

Cross-multiply: 2 * 3 = 2x

Solve for x: x = 3

Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:

1/x + 1/y = 7/12

Substitute x = 3: 1/3 + 1/y = 7/12

Now, solve for y: 1/y = 7/12 - 1/3 1/y = (7/12) - (4/12) 1/y = 3/12

Now, invert both sides of the equation to solve for y: y = 12/3

Simplify: y = 4

So, the solutions to the system of equations are x = 3 and y = 4.