Elimination

[kmomma1999]

Here I am again! This is another three part question in which I think I have the first two answers but not the last. I am also not familiar with the elimination method since this is my first time actually using it!!

The sales representative here tells you they also have two floor plans available, but they only have 38 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.

My answer to this is: x + y = 38

The representative tells you that floor plan #1 sells for $175,000 and floor plan #2 sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in part a.

My answer to this is: 175,000x + 200,000y = 7,200,000

Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Again this last part confuses me. I am not sure how to do the elimination method. I am still going back over my text to try to figure it out, but any help with elimination will be appreciated.

 

[Mrspi]

Here I am again! This is another three part question in which I think I have the first two answers but not the last. I am also not familiar with the elimination method since this is my first time actually using it!!

The sales representative here tells you they also have two floor plans available, but they only have 38 homes available. Write an equation that illustrates the situation. Use x and y to denote floor plan #1 and floor plan #2 respectively.

My answer to this is: x + y = 38

The representative tells you that floor plan #1 sells for $175,000 and floor plan #2 sells for $200,000. She also mentions that all the available houses combined are worth $7,200,000. Write an equation that illustrates this situation. Use the same variables you used in part a.

My answer to this is: 175,000x + 200,000y = 7,200,000

Use elimination to determine how many houses with each floor plan are available. Explain how you arrived at your answer.
Again this last part confuses me. I am not sure how to do the elimination method. I am still going back over my text to try to figure it out, but any help with elimination will be appreciated.

You have two equations in two variables:

x + y = 38
175000x + 200000y = 7200000

If you multiply both sides of the first equation by -200000, your system will look like this:

-200000x - 200000y = -7600000
175000x + 200000y = 7200000

If you ADD the two equations together, do you see that the y variable will be ELIMINATED because -200000y + 200000y is 0?

Add the equations together...and you'll get this:

-25000x = -400000

Ok...finish solving this for x. And once you find the value of x, you can use either of the two original equations to find y (I think using x + y = 38 would be the easiest one to use.)

 

[kmomma1999]

I think I am starting to understand this except for one thing. When you multiplied the first equation by -200000 how did you get the 7600000? I have done the math a few times and I still cannot get that answer.

 

[Deleted member 4993]

38 * (-200,000) = ???

What do you get?

 

[Loren]

x + y = 38
175000x + 200000y = 7200000

It is ok to multiply both sides of the second equation by 1/1000 (or divide by 1000) giving you...

x + y = 38
175x + 200y = 7200

Further, equation 2 can be divided by 25 giving you..

x + y = 38
7x + 8y = 288

You are now in a much better position to spot possibilities for either substitution or addition/subtraction to solve.