Question

There are 13 chickens and pigs in the barn. There are 40 legs
in all (each chicken has two legs and each pig has four legs).
Use substitution to solve the linear system of equations and
determine how many chickens, x, and pigs, y there are.
Express the solution as an ordered pair (x,y).

Answer 1

Answer:

The answer is (6,7).

Step-by-step explanation:

Let's say that x = # of chickens, and y = # of pigs

 If there are 13 animals altogether, that means that

 x + y = 13

 If there are 40 legs together, we know that chickens have 2 legs, while pigs have 4, so the total number of legs would be:

 2x + 4y = 40

 We now have two different equations, with the same two variables, so we can rearrange and substitute one equation into the other to solve. We can rearrange the first equation as:

x + y = 13

 x = 13 - y

 Let's plug this expression for "x" into the second equation:

2(13-y) + 4y = 40

 Now we have an equation with only one variable, so we can use algebra to solve for y:

  26 - 2y + 4y = 40

 

   2y = 14

 

   y = 7, there must be 7 pigs.

 

From the first equation that we rearranged,

 x = 13 - y

 Now that we know the numerical value of "y", we can plug that in:

 

   x = 13 - 7

 x = 6, there must be 6 chickens

So, all in all, there are 6 chickens and 7 pigs, which equals (6,7) as an ordered pair.

Answer 2

Answer:

(6, 7)

Step-by-step explanation:

x+y= 13

2x+4y= 40 ⇒ x+2y = 20 ⇒ 13-y +2y= 20 ⇒ y= 20-13= 7

x= 13-y= 13-7= 6

chickens= 6

pigs= 7