Hi, I am having trouble solving this problem. I have made at least 4-5 attempts on it by now. Can someone please help me out?

Here is the problem: A number consists of two digits. 13 more than 7 times the units digits is 3 times the tens digit. If the digits are reversed, 2 times the new number is 34 less than the original number. Find the number.

Here is one my of attempts:

- Translated each statement into equations:

"13 more than 7 times the units digits is 3 times the tens digit." --> 13+7u=3t

"If the digits are reversed, 2 times the new number is 34 less than the original number" --> 2(10u+t)=10t+u-34

- Made all variables on one side of each equation, and made a system of equations:

3t-7u=13

19u-8t= (-34)

- Solved the system of equations, to solve for u:

3 * (8t+19u = -34) ------> 24t+57u=-102

8 * (3t - 7u = 13) ------> - 24t - 56u=104

113u/113 = -206/113

Therefore, u= -1.8

- Substituted value of u into other equation, to solve for t:

3t-7u=13

3t-7(-1.8)=13

3t+12.6-12.6=13-12.6

3t/3=0.4/3

Therefore, t=0.13

I know all that is wrong. The answer is supposedly 92. I'd appreciate any help, thanks