5x+2y = 19
1x + 4y=13

{x,y} = {25/9,23/9}

Step-by-step explanation:

// Solve equation [2] for the variable  x  

 [2]    x = -4y + 13

// Plug this in for variable  x  in equation [1]

  [1]    5•(-4y+13) + 2y = 19

  [1]     - 18y = -46

// Solve equation [1] for the variable  y  

  [1]    18y = 46  

  [1]    y = 23/9  

// By now we know this much :

   x = -4y+13

   y = 23/9

// Use the  y  value to solve for  x