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Find two numbers such that 6 times the first added to 5 times the second equals -9, and 5 times the first added to 8 times the second equals 4.

I'm not sure how to answer this problem so any help on how to solve this problem would be appreciated.  Thanks!

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2 Answers

Let x = 1st number              

Let y = 2nd number

Read the problem and translate into two sets of simultaneous equations, and solve by elimination:

6x + 5y = -9    multiply every term of this equation by 5   

5x + 8y = 4     multiply every term of this equation by -6

You now have the following equivalent equations where you can eliminate the terms containing x and solve for y.

 30x + 25y = -45

-30x - 48y = -24

   0x -23y = -69     (divide both sides by -23)

            y = 3        plug in 3 for y in either equation and you will find that x = -4

            x = -4

Reread the problem and make sure your two solutions make sense... 



Sometime the equations will become apparent by reciting the question a little differently:

6 times (the first number) added to 5 times (the second number) equal -9

Now let the first number be x and the second be y and use some mathematical symbols:

6x + 5y = -9

Do the same for the next part of the sentence and you will have two simultaneous equations. These can be solved by substitution.


You're welcome. Glad to help.