Answer:
Nolan hitted 8 home runs
Step-by-step explanation:
Let's call the number of home runs that Nolan hitted by N, and that Davis hitted by D.
So, we can write the following equations:
N = 2 * (D - 6)
N + D = 18
Now we can solve the system of equations, using the value of N from the first equation in the second one:
2 * (D - 6) + D = 18
2*D - 12 + D = 18
3*D = 30
D = 10
Now we find N:
N + D = 18
N + 10 = 18
N = 8
So we have that Nolan hitted 8 home runs.
Answer:possible
Step-by-step explanation:
1. Understand what multi-variable equations are.
Two or more linear equations that are grouped together are called a system. That means that a system of linear equations is when two or more linear equations are being solved at the same time.
[1] For example:
• 8x - 3y = -3
• 5x - 2y = -1
These are two linear equations that you must solve at the same time, meaning you must use both equations to solve both equations.
2. Know that you are trying to figure out the values of the variables, or unknowns.
The answer to the linear equations problem is an ordered pair of numbers that make both of the equations true.
In the case of our example, you are trying to find out what numbers ‘x’ and ‘y’ represent that will make both of the equations true.
• In the case of this example, x = -3 and y = -7. Plug them in. 8(-3) - 3(-7) = -3. This is TRUE. 5(-3) -2(-7) = -1. This is also TRUE.
3. Know what a numerical coefficient is.
The numerical coefficient is simply the number that comes before a variable.[2] You will use these numerical coefficients when using the elimination method. In our example equations, the numerical coefficients are:
• 8 and 3 for the first equation; 5 and 2 for the second equation.
4. Understand the difference between solving with elimination and solving with substitution.
When you use elimination to solve a multivariable linear equation, you get rid of one of the variables you are working with (such as ‘x’) so that you can solve the other variable (‘y’). Once you find ‘y’, you can plug it into the equation and solve for ‘x’ (don’t worry, this will be covered in detail in Method 2).
• Substitution, on the other hand, is where you begin working with only one equation so that you can again solve for one variable. Once you solve one equation, you can plug in your findings to the other equation, effectively making one large equation out of your two smaller ones. Again, don’t worry—this will be covered in detail in Method 3.
5. Understand that there can be linear equations that have three or more variables.
Solving for three variables can actually be done in the same way that equations with two variables are solved. You can use elimination and substitution, they will just take a little longer than solving for two, but are the same process.
The table in Part A represents y as a function of x. This means that the value of Y is dependent on the value of X. The table can be represented by an equation that describes the relation of X and Y:
or
By substituting any value of X, you get a specific value of Y based from the given relationship, thus Y is a function of X.
For Part B, the value of f(150) is $470 and it represents the total cost for borrowing a rowboat for 150 hours. By substituting the value of x = 150 into the function, you get the total cost:
