Let A represent Arthur
L represent Lily
-Arthur weighs 34 lb more than Lily, so we need to change this into equation:
A=L+34
-Their combined weight is 180 lb less than 4 times Lily's weight
A+L=4L-180
Then, we need to change A with L+34 into the second equation, and we have
L+34+L=4L-180
2L+34=4L-180
Subtract 2L for both side
2L+34-2L=4L-180-2L
34=2L-180
Add 180 for both side
34+180=2L-180+180
214=2L
Divided 2 for both side
214/2=2L/2
L=107 lb
A=L+34
A=107+34
A=141 lbs
Check:
A=L+34
141=107+34
141=141 OK
A+L=4L-180
141+107=4(107)-180
248=428-180
248=248 True. As a result, Arthur weighs 141 pounds. Hope it help!