甚麼是Linear Equations in Two Unknowns??（20分!!）

Two simultaneous linear equations in two unknown have 0 ,1 or infinite
number of solutions .

The equations should be like these below
ax + by + c = 0 -(1)
dx + ey + f = 0 -(2)


Do you know the slope of the equation can be found by this formula ?
E: ax + by + c = 0
Slope of E is -a/b

Slope of E(1) is -a/b
Slope of E(2) is -d/e

If -a/b = -d/e , what can we conclue@@?
These two equations is parallel
If the line is parallel and do not touch together
there is no intercept points !
There is no solution (having 0 solution)

-a/b = -d/e and these two line touch together ,
how can we find that?

If two parallel lines touch together , the equations of two lines may be same
If
two equations
ax + by + c = 0
dx + ey +f = 0

a = d , b = e , c = f
(after reduction)

For example , two equation
2x + 3y + 4 = 0 (A)
8x + 12y + 16 = 0 (B)
(B) is actually equal to (A) after dividing 4
so there is infinite number of soluions because two lines touch together .

If a =/= d , b =/= e , c=/= f
but -a/b = -d/e , these two lines are parallel but dont touch together .
so there is no soluion

If -a/b =/= -d/e ,
these two lines may intercept with each other ,
since they are linear equations , they have only one intercept point
We can find that :

Two simultaneous linear equations in two unknown have 0 ,1 or infinite
number of solutions

1 solution : a/b =/= d/e
0 soluion : a/b = d/e , a =/= d , b =/= e , c=/= f
infinte number of solutions : a = d , b = e , c = f