2x + y = 2
 4x = 44 + 3y

Solve the first one for y

 2x + y = 2
      y = 2 - 2x

Substitute (2 - 2x) for y in the second equation

 4x = 44 + 3y
 4x = 44 + 3(2 - 2x)
 4x = 44 + 6 - 6x
 4x = 50 - 6x
10x = 50
  x = 5

Substitute into the equation you got when you solved
for y, the one I colored red:


      y = 2 - 2x
      y = 2 - 2(5)
      y = 2 - 10
      y = -8

Solution (x,y) = (5,-8)

----------------------------------------------------

Check by substituting in BOTH original equations:

     2x + y = 2  |    4x = 44 + 3y 
2(5) + (-8) = 2  |  4(5) = 44 + 3(-8)
     10 - 8 = 2  |    20 = 44 - 24
          2 = 2  |    20 = 20

They both check.

Edwin