Answer:
4 and 15
Step-by-step explanation:
Let the two numbers be a and b.
The sum of the two is 19. Therefore:
![a+b=19](https://tex.z-dn.net/?f=a%2Bb%3D19)
One number (let's use a) is 7 <em>more</em> than twice the other. Thus:
![a=7+2b](https://tex.z-dn.net/?f=a%3D7%2B2b)
Solve for the system of equations. Substitute the second equation into the first:
![a+b=19\\(7+2b)+b=19](https://tex.z-dn.net/?f=a%2Bb%3D19%5C%5C%287%2B2b%29%2Bb%3D19)
Subtract 7 from both sides:
![2b+b=12](https://tex.z-dn.net/?f=2b%2Bb%3D12)
Combine like terms:
![3b=12](https://tex.z-dn.net/?f=3b%3D12)
Divide by 3:
![b=4](https://tex.z-dn.net/?f=b%3D4)
So, b is 4.
And since they add up to 19, this means that a is:
![a+b=19\\a+4=19\\a=15](https://tex.z-dn.net/?f=a%2Bb%3D19%5C%5Ca%2B4%3D19%5C%5Ca%3D15)
So our numbers are 4 and 15
And we are done :)