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A and B working together can finish the job in 10 days.
If A works 4 days and B works 3 days, one-third of the job shall be finished.
How many days will it A to finish the job
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There is much easier and more straightforward way to solve the problem, if you correctly choose the unknowns.
Let "a" be the rate-of-work of A, and
let "b" be the rate-of-work of B.
Then from the condition you immediately get these two equations for two unknowns
10a + 10b = 1, (1)
4a + 3b = . (2)
Multiply equation (2) by 3 (both sides). Then you can rewrite the system in the form
10a + 10b = 1, (1')
12a + 9b = 1. (2')
Now, multiply equation (1') by 6, multiply equation (2') by 5 and distract.
In this way you eliminate "a" and obtain a single equation for "b"
60b - 45b = 5 - 4, or 15b = 1, b = .
Then from (1) 10a = 1 - 10b = 1 - = 1 - = ,
Hence, a = .
The rate of "a" is job-per-day; the rate of "b" is job-per-day.
Answer. A will complete the job in 30 days. B will complete the job in 15 days.
The lesson to learn from this solution: choose correctly the unknowns when solving rate-of-work and joint-work problems.