How many solutions exist for the system of equations below?
2 answers:
Answer:
0 (None) solutions
Step-by-step explanation:
This Linear System has no Solution. It means that mathematically speaking, whatever value inserted for x, or y this will not result in an equality, i.e. we'll always have a false value. Like this:
FALSE Because then This Linear System does not have solution.
Geometrically, both equations are parallel lines, so they do not have any common point, i.e. solution. Notice they both have the same slope. Check the graph below.
You might be interested in
Answer:
The functions satisfy the differential equation and linearly independent since W(x)≠0
Therefore the general solution is
Step-by-step explanation:
Given equation is
This Euler Cauchy type differential equation.
So, we can let
Differentiate with respect to x
Again differentiate with respect to x
Putting the value of y, y' and y'' in the differential equation
⇒m²-10m +24=0
⇒m²-6m -4m+24=0
⇒m(m-6)-4(m-6)=0
⇒(m-6)(m-4)=0
⇒m = 6,4
Therefore the auxiliary equation has two distinct and unequal root.
The general solution of this equation is
and
First we compute the Wronskian
=x⁴×6x⁵- x⁶×4x³
=6x⁹-4x⁹
=2x⁹
≠0
The functions satisfy the differential equation and linearly independent since W(x)≠0
Therefore the general solution is