How to solve for one variable in fraction with two variables?

Step 1: Isolate a variable (I isolated y)

1/8y=4-1/2x

y=32-4x

(Remember, when dividing fractions, you actually multiply the numerator by the reciprocal of the denominator).

Step 2: Replace new isolated variable into original double variable equation.

1/2x+(32-4x)=4

Step 3: combine like terms

-7/2x+32=4

(When adding or subtracting fractions, you must have the same denominator! In this case, -4 must be changed to -8/2 to be able to subtract from 1/2)

Step 4: solve for x

-7/2x=-28

x=8

Step 5: plug in known variable for last wanted variable.

1/2(8)+1/8y=4

4+1/8y=4

1/8y=0

y=0

this is 2variables with 1 fraction which means there's unlimited number of solutions.

to get the equalization for the solutions you should isolate Y as Allen said:

1/8y=4-1/2x

y=32-4x

then you give X which ever value you want and it'll give you the answer,

however X can get any value from -infinite to +infinite but not 0 because when it's 0 the original fraction will be devised by 0.

you'll end up with 2 curved lines showing all the possible answers.

you can always use wolframalpha.com to help you with such stuff, tho use it only after you try to solve it, otherwise you won't learn :)

Get one variable on each side of the equals sign. Subtract say 1/2x from both sides so your new equation is 1/8y=-1/2x+4.

y = -4x + 32