Answer:
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.
<em>"The sum of three times four and twice one is 14."</em>
<em>"The sum of twelve and two is 14."</em> True.
<em>"If one is subtracted from twice four, the result is 7."</em>
<em>"If one is subtracted from eight, the result is 7."</em> True.
Therefore, the first number is 4, and the second number is 1.
