Solutions

a. 2x + 3y = 5
   x - 5y = 9  -----> x = 5y + 9

   2(5y + 9) + 3y = 5
   10y + 18 + 3y = 5
   13y + 18 = 5
   13y = -13

     y = -1 

   x = 5y + 9
   x= 5(-1) + 9

      x = 4

   Final Answer: (4, -1)

b. -x + 2y = 3 -----> -x = -2y + 3
    4x -5y = -3 

    4(2y - 3) -5y = -3
    8y - 12 - 5y = -3
    3y - 12 = -3
    3y = 9

     y = 3

    -x = -2y + 3
    -x = -2(3) + 3
    -x = -6 + 3
    -x = -3
  
     x = 3
    
   Final Answer: (3,3)

c. 6x + 4y = 20
   3x + y = 5 ------> y = -3x + 5

   6x + 4y = 20
   6x + 4(-3x + 5) = 5
   6x - 12x + 20 = 5
   -6x + 20 = 5
   -6x = -15

    x = 15/6

   y = -3x + 5
   y = -3(15/6) + 5

   y = -12.5

   Final Answer: (15/6, -12.5)

d. 7x + 8y = 12
   2x + y = 15 -----> y =-2x + 15

   7x + 8(-2x+15) = 12
   7x - 16x + 120 = 12
   -9x = -108

   x = 12

   y = -2x + 15
   y = -2(12) + 15
   y = -24 + 15

   y = -9 

   Final Answer: (12, -9)

e. x + 2y = 2 -----> x = -2y + 2
   4x - 5y = -3

   4(-2x + 2) -5y = -3
   -8x + 8 - 5y = -3
   -13x + 8 = -3
   -13x = -11

    x = 11/13
 
    x = -2y + 2
    -11/13 = -2y + 2
    2.8 = -2y 
    y = -1.4 
   
    Final Answer: (11/13, 1.4)