SOLUTION: How do I solve systems of equations by substitution for example {{{1/2}}}x + {{{3/4}}}y = {{{-7/4}}} {{{5/6}}}x - {{{1/6}}}y = {{{4/3}}}

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Question 604899: How do I solve systems of equations by substitution for example
1%2F2x + 3%2F4y = -7%2F4
5%2F6x - 1%2F6y = 4%2F3
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
        1%2F2x + 3%2F4y = -7%2F4
        5%2F6x - 1%2F6y = 4%2F3

Before you do anything else get rid of those fractions.  

Multiply the first equation through by the LCD of 4:

    4·1%2F2x + 4·3%2F4y = 4·-7%2F4

        2x + 3y = -7

Multiply the second equation through by the LCD of 6:

   6·5%2F6x - 6·1%2F6y = 6·4%2F3

        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