Respuesta :
Cows(m) have 4 legs, chickens(c) have 2. Setting up a system of equations 104=4m+2c and 42=m+c. Solved for c the latter equation becomes 42-m=c. Using substitution in the first equation 104=4m+2(42-m). Distribute: 104=4m+84-2m. Combine like terms: 104=2m+84. Isolate variable term: 104-84=2m. Variable coefficient 1: 20/2=10=m. 42-10=32=c. 10 cows and 32 chickens.
Number of chicken present in the farmyard is equals to 32.
What is the system of equations?
" A System of equations is the finite set of equations for which we find the common solution."
According to the question,
Let x represent number of cows
y represents number of chickens
Two situations are given for which we need to find the system of equations.
Situation 1: There are 42 animals in the farmyard , which can be represented by equation:
x + y = 42
⇒ y = 42 - x _______(1)
Situation 2: Total number of legs of cows and chicken is equals 104.
As we know cow has 4 legs and chicken has 2.
Therefore, equation can be represented by:
4x + 2y =104 __________(2)
Substitute the value of equation (1) in (2) , we get
4(42 -y) + 2y =104
⇒ 168 - 4y + 2y =104
⇒ 2y = 168 -104
⇒ y = 32
Hence, number of chicken present in the farmyard is equals to 32.
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