This problem is so hard I've tried solving it but I keep getting stuck. Could someone help with showing the steps please...

Solve the system of equations for x and y by letting a=1/x and b=1/y, x does not equal 0 and y does not equal 0.

3/x+2/y=2/3
8/x-4/y=2/9

doubling the 1st equation, we have

6/x + 4/y = 4/3
8/x - 4/y = 2/9

add them up to get

14/x = 14/9
x = 9

Now just plug that in to get y=6

Steve your answers are wrong

Never mind I got it sorry

To solve this system of equations, you can use substitution by letting a = 1/x and b = 1/y. Then, rewrite the given equations in terms of a and b.

Let's solve the equations step by step.

1. Start with the given equations:
3/x + 2/y = 2/3 ........(Equation 1)
8/x - 4/y = 2/9 ........(Equation 2)

2. Rewrite the equations in terms of a and b:
3a + 2b = 2/3 ........(Equation 3) [Replace 1/x with a and 1/y with b]
8a - 4b = 2/9 ........(Equation 4) [Replace 1/x with a and 1/y with b]

3. Now we have a system of two equations in terms of a and b:
3a + 2b = 2/3 ........(Equation 3)
8a - 4b = 2/9 ........(Equation 4)

4. We can solve this system of equations using any method we prefer, such as substitution or elimination. Let's use the elimination method here.

Multiply Equation 3 by 4 and Equation 4 by 3, this will eliminate the coefficient of 'b':

12a + 8b = 8/3 ........(Equation 5) [Multiply Equation 3 by 4]
24a - 12b = 2/3 ........(Equation 6) [Multiply Equation 4 by 3]

5. Now, subtract Equation 6 from Equation 5 to eliminate 'b':
(12a + 8b) - (24a - 12b) = (8/3) - (2/3)

Simplify the equation:
12a + 8b - 24a + 12b = 6/3
-12a + 20b = 6/3

6. Simplify further:
8b - 12a = 2

7. Divide both sides of the equation by 4 to simplify:
2b - 3a = 1/2 ........(Equation 7)

8. We now have two equations:
-12a + 20b = 2 ........(Equation 6)
2b - 3a = 1/2 ........(Equation 7)

9. Multiply Equation 7 by 4 to eliminate 'b':
(2b - 3a) * 4 = (1/2) * 4

Simplify the equation:
8b - 12a = 2

10. As we can see, Equation 6 and Equation 10 are the same. This means that we have infinite solutions for this system of equations.

11. To find the values of a and b, we can choose any value for 'a' and find 'b' using either Equation 3 or Equation 4. Let's choose 'a' as 1:

From Equation 3:
3a + 2b = 2/3

Substitute a = 1:
3(1) + 2b = 2/3
3 + 2b = 2/3

Solve for b:
2b = 2/3 - 3
2b = (2 - 9)/3
2b = -7/3
b = (-7/3)(1/2)
b = -7/6

12. Therefore, when a = 1, b = -7/6.

Therefore, the solution to the system of equations is:
a = 1 and b = -7/6.