Question

Miguelle is deciding which type of heating system to put in his house. An oil system costs $2700 to install and

$900 per year to operate. A solar system costs $9000 to install and $200 per year to operate.


Determine your variables
Let=
Let=


2. Create your equations and number them.


3.Solve the linear system using ELIMINATION OR SUBSTITUTION.

Answer 1

Answer: (9, 10800)

Explanation:

We will first let x be the number of years and y be the total cost.

In that case, let's plug in the values for each into the equation y=mx+b, where m is the slope and b is the y-intercept.

The y-intercept will be the value we start with before any years pass, so it will be the installation cost. The slope is how fast the total cost will increase. Since the operation costs have to be added on every year, it will be our slope.

With that in mind, let's create both of our equations:

1. y = 900x + 2700 (Oil system)
2. y = 200x + 9000 (Solar system)

Since y is solved for in the first equation, we can substitute it into the second equation:

`900x + 2700 = 200x + 9000`

`700x + 2700 = 9000` [Subtracting 200x from both sides]

`700x = 6300` [Subtracting 2700 from both sides]

`x = 9` [Dividing both sides by 700]

We can now substitute 9 for x in any equation and solve for y. Here I substituted it into the first one:

`y = 900(9) + 2700`

`y = 8100 + 2700` [Multiplying]

`y = 10800` [Adding]

Hence, the solution to this linear system is (9, 10800).