Understanding the Equations
The given equations are:
1. X + 6/Y = 6
2. 3X - 8/Y = 5
These equations represent relationships between variables X and Y.
Step 1: Rearranging the First Equation
To isolate Y, rearrange the first equation:
- X + 6/Y = 6
- 6/Y = 6 - X
- Y = 6/ (6 - X)
Step 2: Substituting in the Second Equation
Now, substitute the expression for Y into the second equation:
- 3X - 8/(6/(6 - X)) = 5
This simplifies to:
- 3X - (8(6 - X)/6) = 5
Step 3: Simplifying the Second Equation
Now, multiply through by 6 to eliminate the fraction:
- 18X - 8(6 - X) = 30
Expand and simplify:
- 18X - 48 + 8X = 30
- 26X - 48 = 30
- 26X = 78
- X = 3
Step 4: Finding Y
Now, substitute X back into the expression for Y:
- Y = 6/(6 - 3)
- Y = 6/3
- Y = 2
Conclusion
The solution to the equations is:
- X = 3
- Y = 2
These values satisfy both original equations, confirming their correctness.