Step 1) Multiply each side of the equation by #color(red)(2)#:
#color(red)(2)(3x - 8y) = color(red)(2) xx 30#
#(color(red)(2) xx 3x) - (color(red)(2) xx 8y) = 60#
#6x - 16y = 60#
Step 2) Solve each equation for #6x#
#6x - 16y + color(red)(16y) = 60 + color(red)(16y)#
#6x - 0 = 60 + 16y#
#6x = 60 + 16y#
#6x - 5y = -6#
#6x - 5y + color(red)(5y) = -6 + color(red)(5y)#
#6x - 0 = -6 + 5y#
#6x = -6 + 5y#
Step 3) Because both equations are equated to #6x# we can equate the right sides of each equation and solve for #y#:
#60 + 16y = -6 + 5y#
#color(red)(-60) + 60 + 16y - color(blue)(5y) = color(red)(-60) - 6 + 5y - color(blue)(5y)#
#0 + (16 - color(blue)(5))y = -66 + 0#
#11y = -66#
#(11y)/color(red)(11) = -66/color(red)(11)#
#(color(red)(cancel(color(black)(11)))y)/cancel(color(red)(11)) = -6#
#y = -6#
Step 4) Substitute #-6# for #y# in either of the solved equations in Step 4 and solve for #x#. I will use equation 2 but you can use either.
#6x = -6 + 5y# becomes:
#6x = -6 + (5 * -6)#
#6x = -6 - 30#
#6x = -36#
#(6x)/color(red)(6) = -36/color(red)(6)#
#(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) = -6#
#x = -6#
The solution is: #x = -6# and #y = -6# or #(-6, -6)#
