Step 1) Because each equation is already solved for #y# we can equate the right sides of each equation and solve for #x#:
#-4/5x + 10 = 7/5x + 16#
#color(red)(4/5x) - 4/5x + 10 - color(blue)(16) = color(red)(4/5x) + 7/5x + 16 - color(blue)(16)#
#0 - 6 = (color(red)(4/5) + 7/5)x + 0#
#-6 = 11/5x#
#-6 xx color(red)(5)/color(blue)(11) = 11/5x xx color(red)(5)/color(blue)(11)#
#-30/11 = color(blue)(cancel(color(black)(11)))/color(red)(cancel(color(black)(5)))x xx cancel(color(red)(5))/cancel(color(blue)(11))#
#-30/11 = x#
#x = -30/11#
Step 2) Substitute #(-30/11)# for #x# in either of the equations in the problem and calculate #y#:
#y = -4/5x + 10# becomes:
#y = (-4/5 xx -30/11) + 10#
#y = (-4 xx -30)/(5 xx 11) + 10#
#y = (-4 xx -color(red)(cancel(color(black)(30)))6)/(color(red)(cancel(color(black)(5))) xx 11) + 10#
#y = 24/11 + 10#
#y = 24/11 + (11/11 xx 10)#
#y = 24/11 + 110/11#
#y = 134/11#
The solution is: #x = -30/11# and #y = 134/11# or #(-30/11, 134/11)#
