How to calculate least squares regression line by hand

Which steps could be part of the process in algebraically solving the system of equations, y+5x=x^2+10 and y=4x-10

Acoffee shop orders at most $3,500 worth of coffee and tea. the shop needs to make a profit of at least $1,900 on the order. the possible combinations of coffee and tea for this order are given by this system of inequalities, where c = pounds of coffee and t = pounds of tea: 6c + 13t ≤ 3,500 3.50c + 4t ≥ 1,900 which graph's shaded region represents the possible combinations of coffee and tea for this order?

36x2 + 49y2 = 1,764 the foci are located at: (-√13, 0) and (√13,0) (0, -√13) and (0,√13) (-1, 0) and (1, 0)edit: the answer is (- the square root of 13, 0) and (the square root of 13, 0)