Question

You are searching for two integers. The sum of twice the first integer and three times the second integer is nine. At the same time, the sum of three times the first integer and twice the second integer is one. Find the two integers.

Answer 1

Answer: -3 and 5

Explanation:

Let x represent the 1st digit and y represent the 2nd digit. Then,

Eq 1: 2x + 3y = 9 → 3(2x + 3y = 9) → 6x + 9y = 27

Eq 2: 3x + 2y = 1 → -2(3x + 2y = 1) → -6x - 4y = -2

5y = 25

y = 5

Substitute y = 5 into either of the original equations to solve for x:

2x + 3y = 9

2x + 3(5) = 9

2x + 15 = 9

2x = -6

x = -3

Check (using the other original equation):

3x + 2y = 1

3(-3) + 2(5) = 1

-9 + 10 = 1

-1 = 1
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