There are 140 legs on a planet zids have 5 legs and zods have 7 legs h=how many soulutions are there

Number of zids=x
number of zods=y
number of zid legs=5x
number of zod legs=7y

so
5x+7y=140
try to get it into slope intercept from so you can graph is (y=mx+b)
5x+7y=140
subtract 5x from both sides
7y=140-5x
divide both sides by 7
y=20-5/7x
y=-5/7x+20

plug in numbers for x and get numbers for y (you can only plug in multiples of 7 for x so that there are a whole number of zids and since you are counting, x and y must never be negative)

lets try 0 for x

y=-5/7(0)+20
y=20
 so x=0 and y=20 is an answer (if you can have only one of that species)

lets try 7 for x
y=-5/7(7)+20
y=-5+20
y=15

so x=7 and y=15 is an answer

lets try 14 for x

y=-5/7(14)+20
y=-10+20
y=10

so x=14 and y=10 is another answer

lets try 21 for x
y=-5/7(21)+20
y=-15+20
y=5

so x=21 and y=5 is another answer

lets try 28 for x
y=-5/7(28)-20
y=-20+20
y=0

so x=28 and y=0 is an answer (if there can be only one of a species)

if we go further, then y will be negative so the answers are

(x,y)
(0,20)
(7,15)
(14,10)
(21,5)
(28,0)

if it is allowed that only one species exists then there are 5 possible answers
if both must exist simultaneously, then there are only 3 answers