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Svetllana [295]
2 years ago
15

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

Mathematics
1 answer:
stellarik [79]2 years ago
3 0

Answer: (9, 10800)

Step-by-step 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 <em>y=mx+b, </em>where m is the slope and b is the y-intercept.

The y-intercept will be the <u>value we start with before any years pass</u>, so it will be the <u>installation cost</u>. The slope is <u>how fast the total cost will increase</u>. Since the <u>operation costs</u> 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 <em>[Subtracting 200x from both sides]</em>

<em />700x = 6300 <em>[Subtracting 2700 from both sides]</em>

<em />x = 9 <em>[Dividing both sides by 700]</em>

<em />

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 <em>[Multiplying]</em>

<em />y = 10800 <em>[Adding]</em>

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

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