If you simplified a two-equation system and all variables were eliminated, two outcomes are possible.
If the final equation is a true equation, like 3=3, then the system has an <em>infinite number of solutions </em> (the equations graph the same line, and all points appear on both graphs)
If the final solution is a mathematically false equation, like 0=-8, the system has no solution. The lines are parallel and never intersect (have a solution)
The 1st expression is the only one that reproduces the terms being added.
Answer: 45000
Step-by-step explanation:
From the question, we are informed that Patty buys a new car and gets it appraised every few years and that after owning the car for 3 years, its value is $15,000 and further told that after owning the car for 5 years, its value is $9,000.
Let the number of years be x
Let the value of the car be y.
From the first part of the question, we are told that after owning the car for 3 years, its value is $15,000.
Since an inverse variation will be:
x = k/y
3 = k/15000
k = 15000 × 3
k = 45000
Let's confirm the value of k for the second part of the question. After owning the car for 5 years, its value is $9,000. Here, x=5 and y = 9000
x = k/y
x = 45000/9000
x = 5
It's correct.
Therefore, the constant of proportionality is 45000
