# Unknows solution with 3 equations and 2 unknowns

Consider a system with 3 equations and 2 unknowns that has no solutions. List all possible arrangements of the 3 equations as lines on the x-y plane.

I know for a system to have no solution the determinant must be 0. But I do not understand what possible arrangements I can have.

• Hint: intersections, or the lack thereof. May 24, 2017 at 19:56
• An equation with two unknowns is a line one a plane. What arrangement of 3 lines has no intersections? May 24, 2017 at 20:00
• @ja72 is it that there will be two equations where one is a linear combination? May 24, 2017 at 20:30
• Is it possible that you don't understand that the three lines should intersect in the same point to represent a solution? May 24, 2017 at 20:42

Given that equations with two variables (let's assume $x,y \in \mathbb{R}$) are graphically lines on the plane $XY$ then the arrangements are the following: