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We only have cows and ducks in our garden and know that the animals in the garden have 20 legs and 14 eyes. How many cows and ducks do we have

Sagot :

The number of cows and ducks in the garden are 3 and 4 respectively.

Solve the system of linear equations

Let the numbers of cows be x and the number of ducks is y.

Total number of legs=20

Total number of eyes=14

Linear equation for the total number of legs in the garden,

4x+2y=20 -(1)

Linear equation for the total number of eyes in the garden,

2x+2y=14 -(2)

Solve the system of the two linear equations to find the values of x and y.

Subtract equation (1) from equation (2), and we get,

2x=6

[tex]x=\frac{6}{2}\\[/tex]

x=3

Substitute the value of x in equation (1), and we get,

4(3)+2y=20

12+2y=20

2y=20-12

2y=8

[tex]y=\frac{8}{2}\\[/tex]

y=4

Number of cows=3

Number of ducks=4

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