https://file.aiquickdraw.com/mathbot/file/1725994859624l1xvpvej.jpg

The problem presented in the image is a system of equations involving the number of chickens \(x\) and pigs \(y\) raised by a farmer. The two given conditions are:

1. The total number of heads (chickens and pigs together) is 95. Since each animal has one head, we have the equation:
   \[
   x + y = 95
   \]
   
2. The total number of legs is 310. Chickens have 2 legs and pigs have 4 legs, so this leads to the equation:
   \[
   2x + 4y = 310
   \]

Now we can solve this system of equations.

### Step 1: Simplify the second equation
\[
2x + 4y = 310
\]
Dividing the entire equation by 2:
\[
x + 2y = 155
\]

### Step 2: Solve the system
Now we have two equations:
1. \( x + y = 95 \)
2. \( x + 2y = 155 \)

Subtract the first equation from the second:
\[
(x + 2y) - (x + y) = 155 - 95
\]
Simplifying:
\[
y = 60
\]

### Step 3: Substitute \( y = 60 \) into the first equation
\[
x + 60 = 95
\]
Solving for \(x\):
\[
x = 35
\]

### Solution:
- Number of chickens (\(x\)) = 35
- Number of pigs (\(y\)) = 60

Would you like further details or have any questions about the solution?

Here are some related questions:
1. How do you solve systems of equations with substitution?
2. What happens if both animals have the same number of legs?
3. How would the solution change if the total legs were 320?
4. Can this problem be solved graphically?
5. How does eliminating variables simplify solving systems of equations?

**Tip:** When solving systems of equations, look for opportunities to eliminate a variable to simplify the process.

A farmer raises chickens (x) and pigs (y). His animals together have a total of 95 heads and a total of 310 legs. How many chickens and how many pigs does the farmer have?

Solve a system of linear equations to find the number of chickens and pigs a farmer has, given a total of 95 heads and 310 legs. This problem uses algebraic concepts such as elimination to simplify and solve the equations. Suitable for Grades 7-9.

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