Solve the system using the substituion method.
 2x - 5y =  9
-3x +  y = -7

The substitution method works best when there is
a term in one of the variables in one of the 
equations which has a coefficient of 1 or -1.
The second equation has the term "y", which has 
the understood coefficient of 1.

So we solve it for y:

      -3x + y = -7
            y = -7 + 3x

Now we substitute (-7 + 3x) for y in  the first
equation.

        2x - 5y = 9
2x - 5(-7 + 3x) = 9
  2x + 35 - 15x = 9
      -13x + 35 = 9
           -13x = -26
              x = 2

Now substitute (2) for x in

            y = -7 + 3x
            y = -7 + 3(2)
            y = -7 + 6
            y = -1

So the solution is (x,y) = (2,-1)

Edwin