2x + 9y = 29,           (1)
-5x + y = 45            (2)

I will show you how to solve it by applying the Substitution method.

From the equation (2), express "y" via x  y = 45 + 5x. 
Next substitute this expression for "y" into equation (1). Then (1) takes the form

2x + 9*(45+5x) = 29.    (3)

Now simplify and solve it:

2x + 405 + 45x = 29  --->  47x = 29 - 405  --->  47x = -376  --->  x =  = -8.

Thus we got x = -8.  Then from (2) y = 45 + 5x = 45 + 5*(-8) = 5.

Please check yourself the answer.

Answer.  x = -8, y = 5.