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Such an equation has an infinite set of solutions. You can solve the equation for one variable, in terms of the other. Then, by replacing different values for one of the variables, you can get different solutions.
Infinite.
Either an infinite number or none.
No. A pair of linear equation can have 0 solutions (they are parallel), or one solution (they cross at one point) or an infinite number of solutions (they represent the same line).
This is an equation of a line. There are an infinite number of solutions which are all points on the line. It is a linear equation.