Question

Solve the System of Equations

Problem: You have a small ranch with chickens and goats. There are 80 heads and 216 legs. Find the number of both chickens and goats.

Write 2 equations

Solve the System ( use the substitution method )

Graph both equations (use Desmos or graph by hand)

Answer 1

Answer:

Equations: $x+y=80\,,\,2x+4y=216\,\,$

number of chickens = 52

number of goats = 28

Step-by-step explanation:

Given: A small ranch has chickens and goats

Total number of heads = 80

Total number of legs = 216

To find: number of chickens and goats

To draw: the graph

Solution:

Let x denotes number of chickens and y denotes number of goats.

According to the question,

$x+y=80\,\,(i)\\2x+4y=216\,\,(ii)$

From (i), put $x=80-y$ in (ii)

$2(80-y)+4y=216\\160-2y+4y=216\\2y=216-180\\2y=56\\y=\frac{56}{2}=28$

Put $y=28$ in equation (i)

$x+28=80\\x=80-28=52$

So,

number of chickens = 52

number of goats = 28