To solve the problem we solve the equations to know the solution of the system of equations.
A system of equations to have no real solution, the lines of the equations must be parallel to each other.
A system of the equation to be Dependent Consistent System the system must have multiple solutions for which the lines of the equation must be coinciding.
A system of the equation to be Independent Consistent System the system must have one unique solution for which the lines of the equation must intersect at a particular.
The solution of the system of equation is at (-0.1, 0.5).
as the value of y is already given to us, in equation 1, substituting the value of y in equation 2,
[tex]y=-25x-2\\ 5x+1=-25x-2\\ 5x+25x = -2-1\\ 30x = -3\\\\ x = \dfrac{-3}{30}\\\\ x= -0.1[/tex]
Substituting the value of x in equation 1,
[tex]y=5x+1\\ y= 5(-0.1)+1\\ y=-0.5+1\\ y = 0.5[/tex]
Hence, the solution of the system of equation is at (-0.1, 0.5).
The system of equations can be verified by plotting the graph of the equations. As shown in the below image,
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