SOLUTION: 4x-3y=-1 3x-y=-2 Substitution!!! how plz

From the first equation, 

  add 3y to each side -->  4x = -1+3y 

  divide each side by 4 -->  x = (-1+3y)/4 = (-1/4) + (3y/4)



Substitute the right hand side of this last equation for "x" in the 2nd equation:

   3( (-1/4) + (3y/4) )  - y = -2

   

   multiply paren contents by 3 (this is distributive property of multiplication):  

      (-3/4) + (9y/4)  - y = -2

  

   add  3/4 to each side -->  (9y/4) - y = -2 + 3/4

   LHS & RHS over common denom -->   (9y/4)-(4y/4) = (-8/4) + (3/4)



   multiply both sides by 4 -->    9y - 4y = -8 + 3

    combine like terms  --->       5y = -5

    divide both sides by 5 --->     y = -1 



     substitute y=-1 into one of original two equations --> 3x -(-1) = -2

                      3x + 1 = -2

       subtract 1 from both sides -->  3x = -3

          divide both sides by 3  -->   x = -1

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Ans:  x=-1 and y=-1.  

 

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Check by plugging these values into original equations:

     4x - 3y =  4(-1) - 3(-1) = -4 + 3 = -1  (ok)

     3x - y = 3(-1) - (-1) = -3 + 1 = -2  (ok)





You're welcome.  

Since y now has a coefficient of - 1, you can easily solve in terms of y, as follows:
3x - y = - 2
3x = - 2 + y ---- Adding y to each sides
3x + 2 = y ------ Adding 2 to both sides
4x - 3(3x + 2) = - 1 ----- Substituting 3x + 2 for y in eq (i)
4x - 9x - 6 = - 1
- 5x = 5



3(- 1) - y = - 2 -------- Substituting - 1 for x in eq (ii)
- 3 - y = - 2-
- y = - 2 + 3
- y = 1