Question

A theorem from Euclid’s work relates to this particular lesson. The fact that any two lines intersect at exactly one point applies directly to systems of linear equations. Explain how this geometric theorem applies to the algebraic topic of systems of equations.

Answer 1

A system of two linear equations can be thought of as two lines on a plane. The solution to the system of equations (if it exists) is a point that satisfies both equations. That point happens to be the point of intersection of the lines. Since any two different lines that intersect, intersect at exactly one point, then a system of two different equations can have at most one solution.