Question

Write a system of equations to describe the situation below, solve using elimination, and fill in the blanks.

There are two mystery numbers. The sum of 10 times the first number and 5 times the second number is -15. The sum of 6 times the first number and 2 times the second number is -10. What are the two numbers? please explain

Answer 1

-2 and 1

Explanation:

The two "mystery numbers" are described by two relations. We can assign variables to those numbers, and write a system of equations that express the given relations.

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Let x and y represent the first and second mystery numbers, respectively. The first relation tells us ...

10x +5y = -15

The second relation tells us ...

6x +2y = -10

We can reduce both of these equations to lowest terms by factoring out the common factor of 5 from the first one and 2 from the second one:

• 2x +y = -3
• 3x +y = -5

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We are told to solve this using elimination. We can eliminate the y-variable by subtracting the first equation from the second:

(3x +y) -(2x +y) = (-5) -(-3)

x = -2 . . . . . . . . . . simplify

2(-2) +y = -3 . . . . substitute for y

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

The two numbers are -2 and 1.