Its a story problem:

The flying W Ranch raises only cows and horses. There are total 340 animals. The owner prefers horses to cows, so he has 52 more horses than cows.
a. Write two different linear equations to model this situation.
b. Solve the system of linear equations using the substitution method
How many horse live at the ranch?

x=cows

y=horses
x+y=340
y=x+52

Plug in x+52 for your y value on the first equation. Solve for x, and then y.

h + c = 340

h = c + 52

sub the second into the first:
h + c = 340
c+52 + c = 340
2c = 288
c = 144
then h = 144+52 = 196

So 144 cows and 196 horses

a. Let's denote the number of cows as "c" and the number of horses as "h".

From the given information, we can write two linear equations:
1. The total number of animals: c + h = 340
2. The number of horses being 52 more than cows: h = c + 52

b. To solve the system of linear equations using the substitution method, we can substitute the value of h from equation 2 into equation 1.

Substituting h = c + 52 into equation 1:
c + (c + 52) = 340
2c + 52 = 340
2c = 288
c = 144

Now, substitute this value of c back into equation 2 to find h:
h = 144 + 52
h = 196

Therefore, there are 196 horses living at the ranch.

To solve this story problem, we need to model the situation using linear equations and then solve the equations using the substitution method. Let's start by writing the equations.

a. Writing the linear equations:
Let's represent the number of cows as "c" and the number of horses as "h".

From the problem, we know that there are a total of 340 animals, so the first equation is:
c + h = 340

The owner prefers horses to cows, and he has 52 more horses than cows, so the second equation is:
h = c + 52

b. Solving the system of linear equations using the substitution method:
We have two equations:
1. c + h = 340
2. h = c + 52

We can solve the system of equations by substituting the value of "h" from the second equation into the first equation.

From the second equation, h = c + 52. We substitute this into the first equation:

c + (c + 52) = 340

Combining like terms, we get:
2c + 52 = 340

Next, we isolate the variable c by subtracting 52 from both sides:

2c = 340 - 52

Simplifying, we have:
2c = 288

Dividing both sides by 2:
c = 144

Now, we substitute the value of c back into the second equation to find h:

h = 144 + 52
h = 196

Therefore, there are 196 horses living at the ranch.