Solve the systems of equations. Then classify the system as consistent of inconsistent and the equation as dependent of independent.
5x-5y=25
5y-5x=-25
What is the solution of the systems of equation? Is the system consistent or inconsistent? Are the equations dependent of independent

Question

Solve the systems of equations. Then classify the system as consistent of inconsistent and the equation as dependent of independent.
5x-5y=25
5y-5x=-25
What is the solution of the systems of equation? Is the system consistent or inconsistent? Are the equations dependent of independent

anonymous · Answer

Solve for y for both equations to see that they are the same:  y = x - 5

If you graph them they will be the same line (they will coincide.)

The answers are the ordered pairs where the lines intersect... and in this case that is everywhere.  This is a dependent system.  Infinitely many ordered pair solutions... and can be expressed using set notation:

{ (x, y) : where y = x - 5 }  or  (x, x - 5) for short.

anonymous · Answer

Are they consistent?

anonymous · Answer

Consistent if there are solutions...

Inconsistent if there are no solutions...

So yes.