Step 1) Because the first equation is already solved for #y# we can substitute #(4x + 5)# for #y# in the second equation and solve for #x#:
#6x + 11y = 13# becomes:
#6x + 11(4x + 5) = 13#
#6x + (11 xx 4x) + (11 xx 5) = 13#
#6x + 44x + 55 = 13#
#(6 + 44)x + 55 = 13#
#(6 + 44)x + 55 = 13#
#50x + 55 = 13#
#50x + 55 - color(red)(55) = 13 - color(red)(55)#
#50x + 0 = -42#
#50x = -42#
#(50x)/color(red)(50) = -42/color(red)(50)#
#(color(red)(cancel(color(black)(50)))x)/cancel(color(red)(50)) = -21/25#
#x = -21/25#
Step 2) Substitute #-21/25# for #x# in the first equation and calculate #y#:
#y = 4x + 5# becomes:
#y = (4 xx -21/25) + 5#
#y = -84/25 + (25/25 xx 5)#
#y = -84/25 + 125/25#
#y = 41/25#
The Solution Is:
#x = -21/25# and #y = 41/25#
Or
#(-21/25, 41/25)#
