Question

Set up a system of linear equations, and then solve for the indicated quantities.

Three times the smaller of two numbers plus three times the larger number is – 15.
Six times the smaller number minus three times the larger number is – 21.
Find the numbers.
Let x represent the smaller number. Let y represent the larger number.

Answer 1

9514 1404 393

Answer:

• smaller: -4
• larger: -1

Explanation:

Substituting the given variables into the word problem, we have two equations:

3x +3y = -15

6x -3y = -21

Adding these equations eliminates y:

9x = -36

x = -4 . . . . divide by 9

Using this in the first equation, we have ...

3(-4) +3y = -15

-4 +y = -5 . . . . . divide by 3

y = -1 . . . . . . . . . add 4

The smaller number is -4; the larger is -1.