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

The geometric theorem about intersecting lines applies to systems of linear equations because if a system of linear equations has a unique answer, it will be the point of intersection. That is, the point where the two lines intersect, the unique point, is the solution to the system.

Answer 2

For example 
We have y=7-3x
               y=5-2x
and we want to find where the 2 graphs intersect
we add 3x and 2x in the 2 equations
                    3x+y= 7
                    2x+y=5
3x-2x+y-y=7-5
x=2
3*2+y=7
y=7-6
y=1
For x=2, y=1 ⇒ A(2,1) is the point where the 2 graphs intersect

⇒ There is only a point where 2 lines intersect