Hi, can someone please help me solve the following by 
graphing? Thanks in advance! 

1. 3x - 5y = -9
   5x - 6y = -8

Get some points on the first line:

(-8,-3), (-3,0), and (7,6), plot them and draw
a red line through them:

 

Get some points on the second line:

(-10,-7), (-4,-2), and (8,8), plot them and draw
a green line through them:

 


Now we have to guess where the two lines intersect. To do this
draw a blue vertical line through the point of intersection: 

 

Notice that it crosses the x-axis at 2, so the x coordinate of the
point of intersection is 2.


Now draw a horizontal line through the point of intersection: 

 

Notice that it crosses the y-axis at 3, so the y coordinate of the
point of intersection is 3.

So the solution is (x,y) = (2,3)

Check substitute 2 for x and 3 for y in both original equations:

   3x - 5y = -9
   5x - 6y = -8

   3(2) - 5(3) = -9
   5(2) - 6(3) = -8

     6 - 15 = -9
    10 - 18 = -8

         -9 = -9
         -8 = -8

It checks.



2. 4x + 5y = -2
   4y -  x = 11 

Get some points on the first line:

(-8,6), (2,-2), and (7,-6), plot them and draw
a red line through them:

 

Get some points on the second line:

(-7,1), (5,4), and (9,5), plot them and draw
a green line through them:

 


Now we have to guess where the two lines intersect. To do this
draw a blue vertical line through the point of intersection: 

 

Notice that it crosses the x-axis at -3, so the x coordinate of the
point of intersection is -3.


Now draw a horizontal line through the point of intersection: 

 

Notice that it crosses the y-axis at 2, so the y coordinate of the
point of intersection is 2.

So the solution is (x,y) = (-3,2)

Check substitute -3 for x and 2 for y in both original equations:

2. 4x + 5y = -2
   4y -  x = 11

   4(-3) + 5(2) = -2
    4(2) - (-3) = 11

   -12 + 10 = -2
     8 +  3 = 11

         -2 = -2
         11 = 11

It checks.
Edwin