Step 1) Solve each equation for #5x#:

Equation 1)

#5x - y = 17#

#5x - y + color(red)(y) = 17 + color(red)(y)#

#5x - 0 = 17 + y#

#5x = 17 + y#

Equation 2)

#5x + 6y = 3#

#5x + 6y - color(red)(6y) = 3 - color(red)(6y)#

#5x + 0 = 3 - 6y#

#5x = 3 - 6y#

Step 2) Because the left side of both equations is #5x#, we can equation the right sides of each equation and solve for #y#:

#17 + y = 3 - 6y#

#-color(red)(17) + 17 + 1y + color(blue)(6y) = -color(red)(17) + 3 - 6y + color(blue)(6y)#

#0 + (1 + color(blue)(6))y = -14 - 0#

#7y = -14#

#(7y)/color(red)(7) = -14/color(red)(7)#

#(color(red)(cancel(color(black)(7)))y)/cancel(color(red)(7)) = -2#

#y = -2#

Step 3) Substitute #-2# for #y# into either of the equations we solved for #5x# and calculate #x#. I will choose Equation 1 but either equation can be used:

#5x = 17 + y# becomes:

#5x = 17 + (-2)#

#5x = 17 - 2#

#5x = 15#

#(5x)/color(red)(5) = 15/color(red)(5)#

#(color(red)(cancel(color(black)(5)))x)/cancel(color(red)(5)) = 3#

#x = 3#

The solution is: #x = 3# and #y = -2# or #(3, -2)#