4. Algebra: 2nd degree equations and systems of equations

Find the value of the missing leg of this right triangle.

A rectangle has a perimeter of 10 and an area of 6. What is the difference between the lengths of its sides?

A merchant buys oranges. Yesterday, she spent 60 € for some oranges. Today, she spends the same amount but gets an extra 75 oranges, since their price per unit is 4 cents per orange cheaper than yesterday. How many oranges did she buy yesterday?

Multiplying 3 consecutive integers yields 5 times their sum. What is the smallest of these 3 integers?

Which of these systems of equations are compatible determined?

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Which of these systems of equations are inconsistent/incompatible?

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Which of these systems of equations is compatible indetermined?

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