How do you find whether a pair of lines are parallel, perpendicular?

Solve the system of equations. y= 2x y= x^2 - 15

Oscar and julie ashton are celebrating their 15th anniversary by having a reception hall. they have budgeted $4,500 for their reception. if the reception hall charges a $90 cleanup fee plus & 36 per person, find the greatest number of people that they may invite and still stay within their budget.

Prove that quadrilateral is a rhombus.