Answer:
(1.25, - 5 )
Step-by-step explanation:
Given the 2 equations
- 4x + 3y = - 20 → (1)
4x + 2y = - 5 → (2)
Adding the 2 equations term by term will eliminate the x- term
5y = - 25 ( divide both sides by 5 )
y = - 5
Substitute y = - 5 into either of the 2 equations and solve for x
Substituting into (2)
4x + 2(- 5) = - 5, that is
4x - 10 = - 5 ( add 10 to both sides )
4x = 5 ( divide both sides by 4 )
x = = 1.25
Solution is (1.25, - 5 )
Answer:
Step-by-step explanation:
<u>Linear Modeling</u>
Some events can be modeled as linear functions. If we are in a situation where a linear model is suitable, then we need two sample points to make the model and predict unknown behaviors.
The linear function can be expressed in the slope-intercept format:
For the problem at hand, we must pick the adequate variables according to the data provided.
The question states the charge for renting a car is a function of the mileage. It also provides two points from which we can build our model. Let's set the following variables:
c = the charge for renting a car in dollars
x = the distance driven by the businessman in miles
Representing the ordered pair as (x,c), we have the points: (150,79) and (65,63.70). Our model will be expressed as:
We must find the values of m and b with the data provided. Substituting the first point:
Substituting the second point:
Both equations form the following system:
Subtracting both equations:
Note the variable b was canceled out in the operation, leaving only the variable m to solve. Joining like terms:
Solving:
From the first equation
Solving for b:
The model for the problem is:
Now we need to calculate how many miles (x) could be driven for c=$100. From the equation above, substitute c=100
Solve for x:
Rounding to the closest integer: