Answer:
The system of equations is:
x + y = 42
4x + 2y = 120
And there are 24 chickens.
Explanation:
We know that the total number of cows (x) plus the total number of chickens (y) is 42, because Farmer Brown has 42 animals.
We also know that cows (x) have 4 legs and so 4 times the number of cows is the number of cow legs. And chickens (y) have 2 legs, so the number of chickens times two represents the total chicken legs. The sum of 4x + 2y is 120 because there are 120 legs in total.
To solve the system of equations, first solve each equation for y.
In the first equation:
x + y = 42
Subtract x from both sides to isolate y.
y = 42 - x
Second equation:
4x + 2y = 120
Subtract 4x from both sides
2y = 120 - 4x
Divide both sides by 2
y = 60 - 2x
Now that the y's are isolated in both equation, you can put them into 1 equation. Where y = y:
y = 42 - x
y = 60 - 2x
42 - x = 60 - 2x
Add 2x to both sides
42 + x = 60
Subtract 42 from both sides
x = 18
Since x is the number of cows, we know that Farmer Brown has 18 cows.
Now we can substitute the x value into one of the equations:
y = 42 - x
y = 42 - (18)
y = 24
The number of chickens is represented by y, so there are 24 chickens.