Learn Turkish: Dün elektrik yoktu ve makine çalışmıyordu. - Yesterday there was no electricity and the machine was not working.

It combines the verb root çalış (work) with the negative suffix -mı, the continuous suffix -yor (doing), and the past tense suffix -du (was). Read from left to right, it literally builds "work-not-doing-was".

I thought the negative verb suffix was -ma or -me. Why is it -mı in çalışmıyordu?

You are right that it's usually -ma or -me! However, when the continuous suffix -yor comes right after a negative suffix, it forces the negative vowel to narrow into -mı, -mi, -mu, or -mü to match vowel harmony. Because the last vowel in çalış is an undotted 'ı', the negative suffix becomes -mı.

Why does the sentence use yoktu to say "there was no"?

To say "there is not" or "does not exist" in Turkish, we use the word yok. To talk about the past ("there was no"), we simply add the past tense suffix to it. It becomes -tu instead of -du because of consonant harmony (the hard 'k' at the end of yok changes the 'd' to a 't').

Can çalışmak be used for machines? I thought it meant "to study" or "to work" at a job.