The sum of three times a first number and twice a second number is 14. If the second number is subtracted from twice the first number, the result is 7. Find the numbers.

The first number is 4, and the second number is 1.

Step-by-step explanation:

So let's write out everything.

3x + 2y = 14 would be our first equation. The next one is 2x - y = 7. So this is simple.

Let's subtract 2x from the second equation. –y = –2x + 7. Negate everything. y = 2x - 7. Okay. We're going to do some substitution. Substitute 2x - 7 where y is in the first equation.

3x + 2(2x - 7) = 14 => 3x + 4x - 14 = 14 => 7x = 28 => x = 4.

So we know now that x = 4. Let's substitute again and solve.

y = 2(4) - 7 => y = 8 - 7 => y = 1.

Let's double check using the original problem.

"The sum of three times four and twice one is 14."

"The sum of twelve and two is 14." True.

"If one is subtracted from twice four, the result is 7."

"If one is subtracted from eight, the result is 7." True.

Therefore, the first number is 4, and the second number is 1.

7

step-by-step explanation:

the answer would be 7