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

## 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.

# 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.

## Comments

You're welcome. Glad to help.

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