The system has infinitely many solutions. The correct option is C.
<h3>What is a system of equations?</h3>
A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
A linear equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given system of equations is,
-x-4y=2
x+4y=-2
Here a₁ = -1 b₁ = -4 and c₁ = 2
a₂ = 1, b₂ = 4 and c₂ = -2
( a₁/a₂ ) = ( -1 / 1)
( b₁/b₂ ) = ( -1 / 1 )
( c₁ / c₂ ) = ( -1 / 1)
( a₁/a₂ ) = ( b₁/b₂ ) = ( c₁ / c₂ )
From the above condition, we can conclude that the system of the equations will have infinitely many solutions.
Therefore, the system has infinitely many solutions. The correct option is C.
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