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.

Question

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

Answer 1

Use F = first number, S= second number

6F+5S =-9

5F+8S = 4

multiply 2nd by 6 and 1st by 5, then subtract to eliminate 1 variable, F

30F + 48S = 24

30F +25S = -45

23S = 69

S=69/23 = 3 is the 2nd number

5F = 4-(8)(3) = -20

F= -20/5 = -4 is the 1st number

Answer 2

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... 

 

 

Answer 3

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.