x - 1/2y= 6

1/2x + 1/5y = 8

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The given equations are:

`x - 1/2y= 6` --- (i)

`1/2x + 1/5y = 8` --- (ii)

In order to eliminate y from both of the equations, multiply the first equation by 4 and the second equation by 10 and then add them up, to get,

`4x - 2y= 24`

`5x + 2y = 80 `

(+)-----------------------

`9x=104`

`x=104/9`

Put this value of `x` in eq. (i),

`104/9-1/2y=6`

`rArr 1/2y=104/9-6=50/9`

`rArr y=100/9`

Therefore, solution of the set of equations yield:

`x=104/9, y=100/9`

solve for x and y in the given equations:

`x - 1/2y = 6` and `1/2x + 1/5y = 8.`

` `Solve the first equation for x by adding to each side `1/2y.`

`x = 6 + 1/2y.` Now substitute `6+1/2y` for x in second equation.

`1/2 (6 + 1/2y) + 1/5y = 8.` Distribute `1/2.`

`3 + 1/4y + 1/5y = 8.` Combine like terms (adding y's together) and subtract 3 from both sides.

`9/20y = 5` Now multiply both sides by `20/9` to isolate y.

`20/9 (9/20y) = 5* 20/9.`

` ` `y = 100/9` . now substitute the value for y back into equation we isolated x: `x = 6 + 1/2y`

`x = 6 + 1/2*100/9`

`x = 6 + 50/9` since `6 = 54/9` we'll addas a fraction therefore,

`x = 104/9`

**Solution:** `(104/9 , 100/9)`

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