The ratio that rules the file
Lenders divide your total monthly debts, meaning the new housing payment plus cars, student loans, and card minimums, by your gross monthly income. Most programs approve up to somewhere between 43% and 50% depending on compensating factors. That ratio, not a salary threshold, is what qualifies you.
Work an example
Take a household income of $9,000 a month with $700 of existing monthly debt payments. At a 45% DTI cap, total debt can reach $4,050, which leaves about $3,350 a month for housing. At an illustrative 6.5% rate over 30 years, and setting aside roughly a quarter of that for taxes and insurance, the loan supported is somewhere near $400,000. The rate here is an illustration only, not a quote; move it a point in either direction and the answer moves substantially.
Now add a second $700 car payment and $400 of student loans to the same income. The housing allowance drops to about $2,250 and the supportable purchase price falls by well over $100,000.
Income lenders can count
Base salary, documented overtime and bonus history (usually a two-year track record), self-employment net income after expenses, rental income at a haircut, and support payments that can be evidenced. Cash income without a paper trail cannot be counted, which is a planning problem rather than a dead end.
Raise your budget without a raise
Paying off a car or consolidating cards often adds more buying power than a pay rise does, because every dollar of monthly debt removed is a dollar that can go to housing instead. Roughly speaking, $100 a month freed up buys around $15,000-$20,000 of additional loan at rates in the 6-7% range.
Run your own version at /mortgage-calculator/affordability/ before assuming a number either way.