Question 604899
<pre>
        {{{1/2}}}x + {{{3/4}}}y = {{{-7/4}}}
        {{{5/6}}}x - {{{1/6}}}y = {{{4/3}}}

Before you do anything else get rid of those fractions.  

Multiply the first equation through by the LCD of 4:

    4·{{{1/2}}}x + 4·{{{3/4}}}y = 4·{{{-7/4}}}

        2x + 3y = -7

Multiply the second equation through by the LCD of 6:

   6·{{{5/6}}}x - 6·{{{1/6}}}y = 6·{{{4/3}}}

        5x -  y =  8

Now the system is 

        2x + 3y = -7
        5x -  y =  8

Solve the second equation for y

             -y = 8 - 5x

Divide through by -1

              y = -8 + 5x

Substitute -8 + 5x for y in the
first equation:

        2x + 3y = -7
2x + 3(-8 + 5x) = -7
  2x - 24 + 15x = -7
            17x = 17
              x = 1

Substitute 1 for x in 

              y = -8 + 5x
              y = -8 + 5(1)
              y = -8 + 5
              y = -3

Solution: (x,y) = (1,-3)

Edwin</pre>