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