Step 1) Solve each equation for #6y#:
#5x + 6y = 2#
#5x - color(red)(5x) + 6y = 2 - color(red)(5x)#
#0 + 6y = 2 - 5x#
#6y = 2 - 5x#
#-2x + 3y = 37#
#-2x + color(red)(2x) + 3y = 37 + color(red)(2x)#
#0 + 3y = 37 + 2x#
#3y = 37 + 2x#
#color(red)(2) xx 3y = color(red)(2)(37 + 2x)#
#6y = (color(red)(2) xx 37) + (color(red)(2) xx 2x)#
#6y = 74 + 4x#
Step 2) Because the left side of both equations are the same we can equate the right side of both equations and solve for #x#:
#2 - 5x = 74 + 4x#
#2 - color(red)(2) - 5x - color(blue)(4x) = 74 - color(red)(2) + 4x - color(blue)(4x)#
#0 + (-5 - color(blue)(4))x = 72 + 0#
#-9x = 72#
#(-9x)/color(red)(-9) = 72/color(red)(-9)#
#(color(red)(cancel(color(black)(-9)))x)/cancel(color(red)(-9)) = -8#
#x = -8#
Step 3) Substitute #-8# into either of the equations in Step 1 and solve for #y#:
#3y = 37 + 2x# becomes:
#3y = 37 + (-8 xx 2)#
#3y = 37 - 16#
#3y = 21#
#(3y)/color(red)(3) = 21/color(red)(3)#
#(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 7#
#y = 7#
The Solution Is:
#x = -8# and #y = 7#
Or
#(-8, 7)#