Now that the coefficients on y are additive inverses, add (3) to (4):
Multiply by
Substitute the value for x given in (6) into either (1) or (2) (I choose (1)):
The solution set is the ordered pair (0.85, 0.79)
Looks pretty close to me.
You could also have multiplied (1) by 2 and (2) by -3 (or by -2 and 3) so as to eliminate the x instead of the y, but ultimately the result would have been the same. Verification is left as an exercise for the student.