Final answer:
To solve this system, set up and solve two equations representing the number of animals and the number of legs. Substituting the value of one variable into the other equation gives us the values for chickens and cows.
Step-by-step explanation:
To solve this system, let's assign variables to represent the number of chickens and cows the farmer has. Let x represent the number of chickens and y represent the number of cows. We can set up two equations based on the given information.
The first equation represents the total number of animals: x + y = 13.
The second equation represents the total number of legs: 2x + 4y = 34.
To solve this system, we can solve one equation for one variable and substitute that value into the other equation. Let's solve the first equation for x: x = 13 - y.
Now we can substitute this expression for x into the second equation: 2(13 - y) + 4y = 34.
Simplifying the equation gives us: 26 - 2y + 4y = 34.
Combining like terms gives us: 2y = 8.
Dividing both sides by 2 gives us: y = 4.
Now we can substitute this value of y back into the first equation to solve for x: x + 4 = 13.
Subtracting 4 from both sides gives us: x = 9.
Therefore, the farmer has 9 chickens and 4 cows.