Author: Kate Hamilton

POSSIBLE OUTCOMES WHEN SOLVING 3 by 3 EQUATIONS

NO REAL SOLUTIONS
(inconsistent equations)
0 = a number
3 possible ways could happen

UNIQUE SOLUTION
(1 possible solution)
x = , y = , z =

MULTIPLE SOLUTIONS
(dependent equations)
0 = 0
1 possible ways it could happen

3 PARALLEL PLANES
(floating stairs)

2 PARALLEL PLANES and 1 PLANE CROSSING THROUGH (book shelf)

PARALLEL LINES WHERE THE PLANES INTERSECT
(toblerone bar shape)

A LINE OF SOLUTIONS
(Spine of a book)

A PLANE OF SOLUTIONS
(stack of paper)

A LINE OF SOLUTIONS IN A PLANE

2 of the equations will be multiples of the 3rd
BUT
this doesn’t apply to the constants

1 of the equations will be a multiple of another
BUT
this doesn’t apply to the constants

2 of the equations will combine to form the 3rd
BUT
this doesn’t apply to the constants

2 of the equations will combine to form the 3rd
including the constants

2 of the equations will be multiples of the 3rd
including the constants

1 of the equations will be multiple of the 2nd and including the constants. The other plane crosses through them both.

SIMILAR

SIMILAR

SIMILAR

NEVER works with constants

ALWAYS works with constants