Answer
Infinitely many solutions.
Dependent equations.
Work Step by Step
The given equations are
$\Rightarrow 5x-2y-5z=1$ ......(1)
$\Rightarrow 10x-4y-10z=2$ ......(2)
$\Rightarrow 15x-6y-15z=3$ ......(3)
Multiply equation (1) by $-2$.
$\Rightarrow -10x+4y+10z=-2$ ......(4)
Now add equation (2) and (4).
$\Rightarrow 10x-4y-10z-10x+4y+10z=2-2$
Add like terms.
$\Rightarrow 0=0$
Multiply equation (1) by $-3$.
$\Rightarrow -15x+6y+15z=-3$ ......(5)
Now add equation (3) and (5).
$\Rightarrow 15x-6y-15z-15x+6y+15z=3-3$
Add like terms.
$\Rightarrow 0=0$
Hence, the given system of equations is a dependent system, meaning the equations are not truly unique.
There is infinitely many solutions.
